विज्ञान तथा प्रविधि कक्षा ९

ofqfdf :yfg A af6 :yfg B df kU' bf 25.5 km blIf0f kj" { :yfgfGt/0f -displacement_ ePsf]
kQf nufOg\ .

k|Zg -s_ OG6/g]6sf] k|of]u u/L lrq 7.1 df b]vfOPsf] gS;f s;/L x]g{ ;lsG5 < sIffdf
5nkmn ugx'{ f];\ .

k|Zg -v_ pknAw k|ljlwsf] k|of]u u/L tkfO{F klg lrq 7.1 df b]vfOP h:t} s'g} bO' { :yfglarsf]
;fnfvfnf b'/L / Ps :yfgaf6 csfd]{ f k'Ubf xg' ] :yfgfGt/0f kQf nufpgx' f;] \ .

au] / ult (Speed and velocity)

ljm| ofsnfk 7.1

lrq 7.4 n] af6n' Lsf] ofqfsf jm| ddf af6fdf a; ljleGg lbzflt/ df]l8Psf] b]vfp“5 .
tkfO{“n] klg ljBfnosf] rp/df 50 m nfdf] lkmtf (measuring tape_ jf 8f/] Lsf] ;xfotfn]
o:t} lsl;dsf] 6o« fs lgwf/{ 0f ug{x' f];\ . Pp6f :6kjfrsf] ko| fu] u/L sg' } ;fyLnfO{
af6fdf sxL“ lx“8\b} / sxL“ la:tf/} bub' {} Ps 5p] af6 csf{] 5]pdf k'Ug nfus] f] ;do lx;fa
ug'{xf];\ . af6fsf] ljleGg v08df ;fyLsf] rfn s'g sg' lbzflt/ lyof] < :yfgfGt/0f,
cf;} t ju] tyf s'g} lglZrt v08df cf};t ult lx;fa ugx'{ f;] \ .

j:tn' ] ljleGg lbzfdf kl| t ;s] G] 8df kf/ u/]sf] cf;} t b/' L,

c f;} t j]u ( vav)= kf/ u/]sf] b'/L (s) = ... m/s
nfus] f] ;do (t)

j:t'n] lglZrt lbzflt/ kl| t ;s] G] 8df kf/ u/]sf] cf;} t b/' L,

lglZrt lbzfdf kf/ u/s] f] b/' L (s) = m/s …lbzf
pSt b'/L kf/ ug{ nfus] f] ;do (t)
c f;} t ult (vav) =

lrq 7.4 df a;n] :yfg A af6 :yfg F ;Dd lrq 7.4 a;n] kf/ u/s] f] b'/L / o;sf] :yfgfGt/0f
kf/ u/s] f] hDdf b'/L ABCDEF ld6/ x'G5
/ :yfgfGt/0f AF ld6/ pQ/ k"j{ xG' 5 . sg' }
rfn cj:yfdf /xs] f j:tn' ] ljleGg lbzfdf
kf/ u/s] f] hDdf nDafO b/' L -distance_ xf] .
b'/LnfO{ s'g} lglZrt lbzf pNn]v gu/L dfgn]
dfq JoSt ul/g] ePsfn] of] Ps :sn] / kl/df0f
xf] . k|f/lDes :yfgaf6 lglZrt lbzfdf uP/
clGtd :yfgdf k'Ubf j:tn' ] kf/ u/s] f] ;a}
eGbf 5f6] f] b'/L :yfgfGt/0f -displacement_ xf] .
:yfgfGt/0fnfO{ JoSt ubf{ dfg;+Fu} lbzf klg
pNnv] ul/g] ePsfn] of] Ps eS] 6/ kl/df0f xf] .

98 lj1fg tyf k|ljlwM sIff (

b/' L ABCDEF nfO{ pSt b/' L kf/ ug{ nfus] f] ;don] efu ubf{ a]usf] dfg kf| Kt x'G5 . a;n]

af6fsf ljleGg v08x¿df sg' } lglZrt lbzflt/ kf/ u/s] f] b/' LnfO{ pSt b'/L kf/ ug{ nfu]sf]

;don] efu ubf{ ;f] v08df a;sf] ult lbG5 . lrq 7.4 sf] :yfg B df a; k|lt;s]G8 10

ld6/ b/' L kf/ ub}{ kj" {lt/ uO/xs] f] lyof] . :yfg C df a;sf] ult kl/jt{g eP/ k|lt ;]s]G8 20

ld6/ blIf0f k"j{ lbzflt/ ePsf] 5 . af6fsf] DF v08df a;sf] ult 15 ld6/ pQ/k"j{ /xs] f] 5 .

t;y{ j:t'n] k|lt PsfO ;dodf

kf/ ug]{ b'/L pSt j:t'sf] j]u

-speed_ xf] / j:t'n] lglZrt

lbzflt/ kl| tPsfO ;dodf

kf/ u/s] f] b/' L pSt j:ts' f]

ult -velocity_ xf] . olb sg' }

lglZrt lbzflt/ u'l8/xs] f]

j:t' slxn] l56f] / slxn] l9nf] lrq 7.5 ;Gbe{ ljGb' cg';f/ wgfTds ult / C0ffTds ult
u/L u8' \b} 5 eg] To:tf] rfn

c;dfg rfn xG' 5 . pSt j:tn' ] kl| t;]s]G8df kf/ ug{] b'/L c;dfg ult xf] . c;dfg ultn]

lglZrt lbzfdf u'l8/x]sf] j:t'n] nIodf kU' bf To;n] kf/ u/]sf] hDdf b/' LnfO{ pSt b'/L kf/

ug{ nfu]sf] ;don] efu ubf{ k|fKt x'g] ult Tof] j:t'sf] cf};t ult x'G5 .

ju] nfO{ :sn] / kl/df0f / ultnfO{ e]S6/ kl/df0f elgG5 . ultsf] dfgdf kl/jtg{ geP/ sj] n
lbzf kl/jtg{ xbF' f ult kl/jtg{ x'G5 t/ ju] l:y/ /xG5 . lrq 7.5 df b]vfOP h:t} ;Gbe{
laGb' -reference point_ sf cfwf/df s'g} Ps lbzfdf uO/x]sf] j:tn' ] l7s ljk/Lt lbzfdf hfFbf
ult wgfTdsaf6 C0ffTds x'G5 . j:ts' f] ju] ;w}F wgfTds xG' 5 .

k|ju] -Acceleration_

lj|mofsnfk 7.2

Pp6f ;dtn ;tx ePsf] 3 m nfdf] sf7sf] kmNofs lngx' f];\ . pSt kmNofsnfO{ sx] L
58s\ ] agfpg Pp6f 5]plt/ lstfa /fv/] clnslt cUnf] agfpg'xf];\ . kmNofs dfly l;wf
/]vfdf ;lhn} u8' g\ ;Sg] s'g} j:t' lng'xf];\ / 58s\ ] ;txdf u8' fpg'xf];\ . Ps hgf ;fyLn]
:6kjfrsf] ;xfotfn] kT| os] 1 ;]sG] 8sf] hgfj ug'{xf;] \ / csf]{ ;fyLn] kmNofsdf u'8\b} u/]sf]
j:t' k'us] f] :yfgdf lrxg\ nufpg'xf;] \ . rfn s:tf] xG' 5, cjnfs] g ug'{xf];\ .

rfn cj:yfdf /x]sf j:tx' ¿df ;dfg ult gxg' ;S5 . u'l8/x]sf a;sf] ult sxLF a9\b} a9\b}
hfg] / sxLF 36\b} 36b\ } hfg] x'G5 . Psgf;sf] le/fnf] ;txdf kY[ jLsf] u'?Tj ann] u8' b\ } u/s] f]
j:t'df kl| t;]s]G8 ult a9b\ } hfG5 . To:t} kY[ jLsf] ;txdf :jtGq ¿kn] vl;/xs] f] j:ts' f] ult
kl| t;]sG] 8 9.8 m/s n] a9\5 . k|lt PsfO ;dodf xg' ] ult kl/jt{gnfO{ kj| ]u elgG5 . o;sf]
SI PsfO m/s2 xf] .

lj1fg tyf kl| jlwM sIff ( 99

clGtd ult (v) – ;?' sf] ult (u)
k |ju] ( a) = ;do (t)

kY[ jLsf] u?' Tjansf] sf/0f :jtGq ¿kdf vl;/xs] f] j:td' f
pTkGg x'g] kj| ]u u?' Tj k|ju] xf] . o;nfO{ 'g' n] ;ªs\ ]t
ul/G5 . k[YjLsf] ;txdf o;sf] cf;} t dfg 9.8 m/s2 xG' 5 .

u8' \b} u/]sf] a;df lj:tf/} as]| nufpbF f o;sf] ult 36b\ }
u/]sf] cge' j ug{ ;lsG5 . s'g} rfn cj:yfdf /x]sf]
j:ts' f] k|ltPsfO ;dodf ult 36\g] b/nfO{ ultxf| ;
-retardation_ elgG5 . o;nfO{ C0ffTds k|j]u elgG5 .

5nkmnsf] k|Zg

lrq 7.7 df :jtGq v;fOsf] cjnf]sgaf6 kf| Kt x'g] tYofª\s lrq 7.6 =:jtGq ¿kn] vl;/xs] f] j:ts' f]

lbOPsf] 5 . pSt tYofª\snfO{ cfwf/ dfgL tn ul/Psf 3s ;Ddsf] rfn

lx;fax¿af6 s] lgisif{ lgsfNg ;lsG5 <

cf;} t ult (vav) = cf;} t ult (vav) =
lglZrt lbzfdf kf/ u/s] f] b/' L (s)
;'?sf] ult -u_ ± clGtd ult -v_

pSt b/' L kf/ ug{ nfu]sf] ;do (t) (2)

= 44.1 = (0+29.4)
3 2

= 14.7m/s k[YjLsf] s]Gbl| t/ = 14.7 m/sk[YjLsf] sG] bl| t/

:jtGq ¿kn] vl;/xs] f] j:ts' f] rfnsf] lbzf lglZrt eP tfklg kl| t ;s] ]G8 kf/ ug]{ b'/L km/s
km/s x'G5 h'g c;dfg ult xf] . pSt vl;/xs] f] j:tn' ] kf/ u/s] f] hDdf b/' LnfO{ nfus] f] ;don]
efu ubf{ cf};t ult kf| Kt xG' 5 . :jtGq v;fOsf] cj:yfdf j:t'sf] k|ju] eg] k|lt ;s]G8 ;dfg
xG' 5 . j:t' ;dfg kj| u] n] l;wf /]vfdf v:bf jf u8' \bf j:t'sf] k|f/lDes ult / clGtd ultsf]
dWosn] pSt j:ts' f] cf};t ult lbG5 . t;y{ l;wf /]vLo rfndf ;dfg k|j]un] ePsf] j:ts' f
nflu

cf;} t u lt (Vav) = ;'?sf] ult -u_2± clGtd ult -v_

l;wf /]vLo rfnsf ;dLs/0fx¿ -Equations of linear motion_

l;wf /]vLo rfnsf ;dLs/0fdf ;dfjz] r/ /flzx¿ s, u, v, a, t cGt{ut l;wf /v] Lo rfndf
/xs] f] j:ts' f nflu 'u' n] pSt j:ts' f] ;?' sf] ult, 'v' n] j:t'sf] clGtd ult, 'a' n] j:td' f

100 lj1fg tyf k|ljlwM sIff (

pTkGg kj| ]u, 't' n] j:t' rfn cj:yfdf xF'bfsf] ;do / 's' n] j:t' rfndf xFb' f ;'?sf] :yfgaf6
ePsf] :yfgfGt/0fnfO{ hgfp5F g\ .

1. l;wf /]vLo rfnsf nflu ;?' sf] ult -u_, clGtd ult -v_, k|ju] -a_ / ;do -t_ ;DaGwL
;dLs/0f

dfgf}F, sg' } l;wf /]vLo rfndf /xs] f] j:ts' f] ;?' sf] ult -u_ Psgf;n] kl/jt{g x'Fb}
sx] L ;do -t_ kl5 clGtd ult -v_ df kl/0ft eof] .

clGtd ult – ;'?sf] ult lrq 7.8
k|j u] sf] k l/efiffc g;' f/, k|ju] = ;do

a = (v-u)

t

at = v - u

v = u+at ………………….. (i)

pbfx/0f 7.1

lqej' g cGt/fl{ i6o« ljdfg:ynaf6 p8g\ ] j|mddf l:y/ cj:yfaf6 wfjgdfu{df pQ/ lbzflt/
u'8s] f] xjfOh{ xfh 40 s kl5 p8\of] . xjfO{hxfh u8' b\ fsf] ;dfg kj| u] 0.75 m/s2 lyof] . pSt
xjfO{hxfh l7s hldgaf6 p8\g' k"j{sf] ult lx;fa ug{x' f];\ M

pbfx/0fdf xjfO{hxfhsf nflu lbOPsf] ljj/0f cg';f/,

xjfO{hxfhsf] ;?' sf] ult -u_ = 0 (\ l:y/ cj:yfaf6

u8' ]sf_]

Psgf;n] ult kl/jt{g ePsf] ;do (t) = 40 s

xjfOh{ xfhsf] kj| ]u (a) = + 0.75 m/s2

clGtd ult -v_ = ? lrq 7.7
rfnsf] ;dLs/0f k|of]u ubf{,

v = u + at

v = 0 + 0.75 × 40

v = 30 m/s (pQ/)

xjfO{hxfh l7s hldgaf6 p8g\ ' k"j{ 30 m/s pQ/ sf] ultn] u'l8/x]sf] lyof] .

lj1fg tyf k|ljlwM sIff ( 101

2. l;wf /]vLo rfnsf nflu ;'?sf] ult -u_, clGtd ult -v_, k|ju] -a_ / :yfgfGt/0f -s_
;DaGwL ;dLs/0f

dfgf,F} s'g} l;wf /]vLo rfndf /xs] f] j:t' Ps :yfgaf6 csf]{ :yfgdf :yfgfGt/0f -s_
eof] . :yfgfGt/0f xF'bf ;'?sf] ult -u_ Psgf;n] kl/jtg{ xb'F } sx] L ;do -t_ kl5 lglZrt
clGtd ult -v_ kf| Kt u¥of] .

;dfg ¿kn] ult kl/jt{g eO/x]sf] cj:yfdf

lglZrt lbzflt/ kf/ u/s] f] b/' L = cf;} t ult × ;do

3. l;wf /]vLo rfnsf nflu ;'?sf] ult -u_, ;do -t_, k|ju] -a_ / :yfgfGt/0f -s_ ;DaGwL
;dLs/0f

dfgfF} sg' } l;wf /]vLo rfndf /xs] f] j:t' ;dfg k|j]u -a_ n] Ps :yfgaf6 csf]{ :yfgdf
:yfgfGt/0f -s_ eof] . kj| u] pTkGg xb'F fsf] ;do -t_ df pSt j:tsf] ;?' sf] ult -u_
kl/jt{g eO{ clGtd ult -v_ aGof] .

;dLs/0f (ii) cg';f/,

sg' } j:t' :jtGq ¿kn] k[YjLdf vl;/x]

sf] cj:yfdf -xfjfsf] cj/fw] guGo

dfGbf_ 7f8f] l;wf /]vLo rfnsf

;dLs/0fx¿ M
v = u + gt
v2 = u2 + 2gh
(iv) h = ut+21 gt2

lrq 7.10 rp/sf] kfl/:ylts k4lt

102 lj1fg tyf k|ljlwM sIff (

pbfx/0f 7.2

kj" { klZrd /fhdfu{sf] l;wf v08df Pp6f l:y/ cj:yfaf6 rNg ;?' u/]sf] df]6/;fOsn 0.5 m/s2
sf] ;dfg kj| ]un] 400 m k"j{lt/ ul' 8;s]kl5 rfnsn] a|]ssf] k|of]u u/] . pSt df6] /;fOsnsf] ult
4 s ;Dd Psgf;n] 36\b} 6 m/s2 sf] ultx|f; pTkGg eof] . ;?' sf] :yfgaf6 ePsf] df]6/;fOsnsf]
:yfgfGt/0f lx;fa ugx{' f];\ M

pbfx/0fdf df]6/;fOsnsf nflu lbOPsf] ljj/0f cg;' f/,

klxnf] v08sf nflu bf;] |f] v08sf nflu
;'?sf] ult -u_ = 0 ;?' sf] ult -u_ = klxnf] v08sf] clGtd ult = 20 m/s kj" {
k|ju] -a_ = + 0.5 m/s2 ;do -t_ = 4 s
:yfgfGt/0f -s_ = 400 m kj" { kj| ]u -a_ = - 6 m/s2
clGtd ult -v_ = ? :yfgfGt/0f -s_ = ?
rfnsf] ;dLs/0f k|of]u ubf,{ rfnsf] ;dLs/0f ko| f]u ubf{,

v2 = u2 + 2as s = ut + 1at2
v2 = 0 + 2 × 0.5 × 400 2

v2=400 s= 20 × 4 –1 × 6 × 42
2
∴ v=20 m/s k\"j{
s= 80-48

∴ s= 32 m k\j" {

;'?sf] :yfgaf6 ePsf] df6] /;fOsnsf] :yfgfGt/0f = klxnf] v08sf] :yfgfGt/0f + bf];|f]
v08sf] :yfgfGt/0f

= 400 + 32 = 432 m k"j\ {

l;wf /]vLo rfnsf uf| km (Graph of linear motion)

:yfgfGt/0f ;do u|fkm -displacement- time graph_

;/' hn] cfkm\ gf] ljBfnodf cfof]hgf ul/Psf] bf8} kl| tofl] utfdf bf8} sf] 6o« fsdf /f]xgnfO{
ljgoeGbf sx] L cufl8 bv] ] . Ps}l5g kl5 ljgon] /f]xgnfO{ kl5 kf/] . tn lrq 7.10 df b'j}
hgf Psgf;n] cfcfk\mgf] ultn] bub' fs{ f] ;donfO{ x- cIf -x-axis_ / :yfgfGt/0fnfO{ y- cIf
-y-axis_ df /fv/] lvlrPsf] uf| km lbOPsf] 5 .

lj1fg tyf kl| jlwM sIff ( 103

lrq 7.8 bf}8sf] 6«ofsdf ljBfyLx{ ¿ bu'b{} lrq 7.9 bf8} sf] :yfgfGt/0f ;do uf| km

k|Zgx¿

1. dflysf] :yfgfGt/0f ;do uf| kmdf b]vfOPsf] s'g /v] fn] /f]xgsf] rfn / s'g /v] fn] ljgosf]
rfn hgfpF5 <

2. ;?' df /fx] g ljgoeGbf slt b/' Ln] cufl8 /xs] f lyP <

3. bf}8sf jm| ddf slt ;sG] 8kl5 ljgon] /fx] gnfO{ lht5] g\ <

4, /v] f AB / CD dWo] s'g /]vfsf] es' fj -le/fnf]kgf_ a9L 5 < /v] fx¿sf] em' sfj /
;DalGwt JolStsf] ultlar s:tf] ;DaGw /x]sf] 5 <

l;wf /]vLo rfnsf uf| km k|ofu] u/]/ j:t'sf] rfnaf/] j0fg{ ug{ ;lsG5 . sg' } j:t'sf] :yfgfGt/0f
/ ;DaGwLt :yfgfGt/0fsf nflu nfu]sf] ;dolarsf] ;DaGwnfO{ :yfgfGt/0f ;do u|fkmdf
b]vfOG5 . :yfgfGt/0f ;do u|fkmsf nflu nfus] f] ;donfO{ X- cIfdf / ;DaGwLt :yfgfGt/0fnfO{
Y- cIfdf k|:t't ul/G5 . :yfgfGt/0f ;do uf| kmsf] em' sfjn] rfn cj:yfdf /xs] f] j:t'sf] ult
hgfp5F . bO' {cf6] f :yfgfGt/0f ;do /v] fx¿sf] e'msfjsf] t'ngf u/]/ l56f] jf l9nf] u'l8/xs] f]
j:t' yfxf kfpg ;lsG5 . tn' gfTds ¿kdf em' sfj a9L ePdf j:ts' f] ult klg a9L x'G5 /
em' sfj sd x'bF f ult klg sd x'G5 . bO' { /]vfx¿ sfl6Psf] :yfgdf j:t'x¿sf] kf/ u/]sf] b/' L
a/fa/ xG' 5 .

ljm| ofsnfk 7.3

Psgf;sf] ;dtn ;txdf tn lrqdf bv] fOP h:t} Ps Ps ld6/sf] b/' Ldf lrxg\ nufP/
6 m nfdf] 6«ofs tof/ kfgx{' f;] \ . Pp6f Aof6L« af6 rNg] 6fo] sf/ lnP/ u8' fpgx' f];\ . 6fo] sf/
pknAw gePdf lrNnf] ;dtn ;txdf es'G8f] u'8fpgx' f;] \ . rfn ;?' eP;“u} :6kjfr lyRgx' f;] \ .
kT| o]s Ps ld6/sf] b'/L ylkb“ } hfb“ f nfu]sf] ;do l6Kg'xf;] \ M

104 lj1fg tyf k|ljlwM sIff (

lrq 7.10 6f]osf/sf] rfnsf] cjnfs] g

tflnsf M :yfgfGt/0f ;do tYofª\s

;do -x–cIfdf_ ============== ============== ============== ==============
=============
:yfgfGt/0f -y– cIfdf_ ============== ============== ==============

k|fKt tYofª\ssf cfwf/df lrq 7.13 df bv] fOP h:t} u|fkm lvrL /]vfsf] e'msfj lx;fa
ug'{xf];\ . pbfx/0fsf nflu

:yfgfGt/0f ;do tYofªs\

t (s) 1 2 3 4
x (m) 4 8 12 16

;q" cg';f/ lrq 7.11 dfg ultn] ul' 8/xs] f] j:ts' f] lj:yfkg
e'msfj (slope) = r9fj (Rise) ;do u|fkm
lj:tf/ (Run)

:yfgfGt/0f–;do u|fkmdf,

em' sfj ≠ :yfgdf cfPsf] cGt/ (∆x)
;dodf cfPsf] cGt/ (∆t)

hxfF '∆' u|Ls efiffsf] cIf/ xf] . o;n] ePsf] kl/jtg{ nfO{ hgfp5F .

em' sfj = r9fj (x2 – x1 )
lj:tf/ (t2 – t1)
em' sfj = 82 = 4m/s

pbfx/0f 7.3

tnsf] u|fkmdf Pp6f df6] /;fOsnsf] rfnnfO{ tLgcf]6f v08df b]vfOPsf] 5 . pSt v08x¿df
df6] /;fOsnsf] cf;} t ult / ultsf] cj:yf klg nV] g'xf];\ M
u|fkmcg;' f/, AB v08df
cf};t ult Ö :yfgfGt/0f ;do /]vfsf] em' sfj -VAB_

lj1fg tyf k|ljlwM sIff ( 105

Ö laGb' G (10,200) / ljGb' E (30,600) larsf] e'msfj

Ö ∆x Ötx2 –2 –t1x1 Ö 600 –102 00 Ö 400
∆t 30 – 20

VAB= 20 m/s

df]6/;fOsn cufl8 a9b\ } hfFbf ;do;uF }

kf/ u/s] f] b'/L klg Psgf;n] a9]sf] 5 .

df]6/;fOsn ;dfg ultn] ul' 8/xs] f] 5 .

BC v08df cf;} t ult Ö 0 m/s,
df6] /;fOsn l:y/ cj:yfdf /x]sf] 5 .

lrq g= 7.12

CD v08df cf;} t ult -VCD_ Ö :yfgfGt/0f ;do /]vfsf] em' sfj

Ö laGb' H (80,600) / laGb' J (120,200) larsf] em' sfj

Ö ∆x Ö x2 – x1 Ö 200 – 400 Ö – 400
∆t t2 – t1 120 – 80 40


VCD = –10 m/s

hxfF C0ffTds lrx\gn] df6] /;fOsnsf] rfn dn" laGb -origin_ lt/ 5 cyf{t\ kms/{] ;'?sf]

:yfglt/ cfO/x]sf] eGg] hgfp5F . df6] /;fOsn k5fl8 kmlsb{ F} ubf{ a9s] f] ;do;Fu} Psgf;n]

b/' L kf/ ub{} kmss]{ f] 5 . o; v08df klg df6] /;fOsn ;dfg ultn] u'l8/x]sf] 5 .

ljm| ofsnfk 7.4

lbOPsf] uf| kmn] Pp6f l;wf af6fdf Psgf;n] lxl“ 8/x]sf] dflg;nfO{ Pp6f ss' '/n] nv6] \g vf]Hbf
10s ;dofjlwdf dflg;sf] rfnnfO{ bv] fOPsf] 5 . pSt dflg;sf] rfn j0f{g ug{'xf;] \ . ;fyLx¿
;d"xdf ldnL pSt rfn kb| z{g ug'x{ f];\ .

106 lrq g= 7.13
lj1fg tyf k|ljlwM sIff (

v08 AE v08 EH v08 HI

:yfgfGt/0f ;do /]vfsf] e'msfj :yfgfGt/0f ;do /v] fsf] s'g} bO' { =================

hg' ;s' } bO' { laGbl' ar ;dfg laGb'df e'msfj km/s km/s

x- cIf;Fu ;dfgfGt/ :yfgfGt/0f ;do /]vfn] ;do a9b\ f klg j:t'sf] b/' L ga9]sf] cyf{t\ j:t'
l:y/ cj:yfdf /x]sf] hgfp5F . em' sfj;lxtsf] l;wf :yfgfGt/0f ;do /]vfn] rfn cj:yfdf
/x]sf] j:t' ;dfg ultn] uO/x]sf] hgfp5F . olb :yfgfGt/0f ;do u|fkmdf jjm| /v] f ePdf rfn
cj:yfdf /x]sf] j:t'sf] ult c;dfg x'G5 .

lrq g= 7.14

ult – ;do u|fkm (velocity- time graph)

ljm| ofsnfk 7.5

tn tflnsfdf lbOPsf tYofªs\ sf cfwf/df ;donfO{ x-cIfdf / ;DalGwt ultnfO{ y-cIfdf
/fvL 5'6\6f56' 6\ } uf| km lvRgx' f;] \ .

tflnsf 01 2 3 45
55 5 5 55
;do (s)
ult (m/s)

tflnsf

;do (s) 0 1 2 3 4 5
ult (m/s) 0 9.8 19.6 29.4 39.2 49

lj1fg tyf kl| jlwM sIff ( tflnsf
;do (s) 0 1 2 3 4 5
ult (m/s) 0 2 6 12 20 30

107

ca tkfOnF ] lvRg' ePsf] ult ;do uf| kmsf] cWoog u/L ljZn]if0f ugx'{ f];\ .

u|fkm ult ;do /]vf ult ;do /v] f ljZn]if0f

cfsf/ e'msfj

klxnf] ================== ================== j:ts' f] ult -;dfg÷Psgf;n] kl/jt{g, ========_=

bf];f| ] ================= ====================== ult ;do /]vfsf s'g} b'O{ laGb'larsf] e'msfj
-;dfg÷c;dfg_ ========

em' sfj / kj| u] sf] ;DaGw =======

t];|f] ============ ==================== Psgf;n] ult kl/jt{g x'bF f / c;dfg ¿kn]
ult kl/jtg{ xbF' f em' sfjdf bl] vPsf] cGt/
==========

sg' } j:ts' f] ult / ;DalGwt ;dolarsf] ;DaGwnfO{ ult ;do uf| kmdf b]vfOG5 . :yfgfGt/0f
;do uf| km h:t} ult ;do u|fkmn] klg j:ts' f] rfn;DaGwL ljleGg hfgsf/Lx¿ lbG5 . o:tf]
uf| kmsf] cjnfs] gaf6 j:t' l:y/ /x]sf,] ;dfg ultdf cufl8 a9s] f]÷/f]lsg vf]h]sf] h:tf
hfgsf/Lx¿ yfxf kfpg ;lsG5 . ult ;do uf| kmdf, ;donfO{ X- cIfdf / ultnfO{ Y- cIfdf
k:| t't ul/G5 . ult ;do /]vfsf] em' sfjn] rfn cj:yfdf /xs] f] j:t'sf] kj| u] lbG5 . bO' c{ f]6f
ult ;do /]vfx¿sf] em' sfjsf] tn' gf u/]/ ult kl/jtg{ sf] b/df /xs] f] leGgtfaf/] hfgsf/L
kfpg ;lsG5 .

x- cIf;Fu ;dfgfGt/ ult ;do /]vfn] ;do a9b\ f klg j:ts' f] ult ga9]sf] cyft{ \ j:t' ;dfg
ultn] ljgf k|ju] uO/xs] f] hgfp5F . em' sfj;lxtsf] l;wf ult–;do /]vfn] rfn cj:yfdf
/xs] f] j:t' ;dfg k|ju] n] uO/x]sf] hgfp5F . olb :yfgfGt/0f ;do u|fkmdf jqm /v] f ePdf rfn
cj:yfdf /xs] f] j:ts' f] ult c;dfg xG' 5 .

lrq 7.15

108 lj1fg tyf kl| jlwM sIff (

lj|mofsnfk 7.6

lbOPsf] ult–;do uf| kmsf] cWoog
u/L tnsf] tflnsf k"/f ug'{xf;] \ .

;dfg kj| ]u ePsf v08x¿dWo]
sg' v08df j:t'sf] ult tLj| ?kn]
kl/jtg{ ePsf] 5 <

;dfg ultsf] v08 lrq 7.16

;dfg kj| ]usf] v08 c;dfg k|j]usf] v08 ultxf| ;sf] v08

BC / …… ……. / …… ……./ …… ……. / ……

;dfg kj| u] ePsf v0x¿ AB, GH dWo] GH v08df ult ;do /]vfsf] em' sfj AB v08df eGbf
a9L 5 . pSt j:ts' f] ult GH v08df tLj| ¿kn] kl/jtg{ ePsf] 5 .

rfn;DaGwL Go6' gsf lgodx¿ -Newton's laws of motion_

;/ cfOHofs Go6" g -Sir Issac Newton_ Ps ef}ltszf:qL / ul0ft1 lyP . pgn] ;g\ 1687
df j:ts' f] rfn;DaGwL tLgcf6] f lgodx¿ kl| tkfbg u/s] f lyP . Go6' gsf] rfn;DaGwL klxnf]
lgodn] an / Ogl;{ofsf] kl/efiff lbG5 . bf];|f] lgodn] ansf] k|of]u / j:t'sf] lk08;Fu k|ju] sf]
;DaGwsf] j0f{g ub5{ . o;sf] ko| f]uaf6 ansf] dfkg ug{ ;lsG5 . Go"6gsf] t;] |f] lgodn] b'O{
anx¿ Úlj|mofÚ -action_ / Úkl| tlj|mofÚ -reaction_ larsf] ;DaGw :yflkt ub{5 . o;n] ansf]
u'0f atfp5F .

Ogl;o{ f -Inertia_

tn lbOPsf 36gfx¿df ;DalGwt tYo / sf/0f kQf nufpg 5nkmn ugx{' f;] \ .

1. lkª vN] g] qmddf o;nfO{ dRrfpg / dRrfP/ 5f]8s] f] lkª l:y/ cj:yfdf cfpg s]xL ;do
nfU5 .

2. l:jr cg ug{] ljlQs} ljBt' \ kªv\ f hf]8n] 3'Db}g / 3'ld/x]sf] kª\vfsf] l:jr ckm ug]{
lalQs} /f]lsb}g .

ha s'g} j:t'df nfUg] anx¿ ;Gt'lnt xG' 5g\, ToxfF j:ts' f] cj:yf -ult jf lbzf_ df sg' }
kl/jtg{ x'Fb}g . j:ts' f] cj:yf kl/jt{g x'g jf j:t' ;g{ pSt j:td' f c;Gtl' nt anx¿ nfUg'
kb5{ . j:t'n] c;Gtl' nt ansf] ko| f]uaf6 o;sf] cj:yfdf ug{ vfl] hg] kl/jtg{ sf] cj/f]w u5{ .
c;Gtl' nt ansf] dfqf lgs} sd ePdf Ps} l5gdf l:y/ cj:yfdf ePsf] j:t'nfO{ rfndf
/ rfndf ePsf] j:t'nfO{ l:y/ cj:yfdf Nofpg ;lsbF g} . l:y/ cj:yfdf /x]sf] j:t' l:y/
cj:yfd} /xg vf]H5 / rfn cj:yfdf /xs] f] j:t' ;dfg ultn] pxL lbzfdf rfndf /xg vf]H5 .

lj1fg tyf kl| jlwM sIff ( 109

s'g} klg j:t'n] o;sf] cj:yfdf ug{ vf]lhg] kl/jtg{ sf] cj/f]w u/L oyfl:yltdf /lx/xg vf]Hg]
u0' fnfO{ Ogl;{of elgG5 .

lrq 7.17 uf]8fn] xfg]/ km' 6an u8' fPsf ] lrq 7.18 9ª' u\ fdf uf8] f 7fl] Ssbf

lj|mofsnfk 7.7

Pp6f 6]andf /flvPsf pl;g]sf] / gpl;g]sf] km' nnfO{ 6a] naf6 cfkm\ gf] xftdf glnOsg 5§' ofpg
b'jn} fO{ j|mdzM l:kg -spin_ ugx{' f];\ . k|Tos] n] rfn cj:yfaf6 l:y/ cj:yfdf cfpb“ fsf] If0fsf]
cjnfs] g u/L kf| Kt glthfnfO{ tnsf] tflnsfsf cfwf/df kl' i6 ug{'xf;] \ .

cjnfs] g glthf AofVof
================= ==================
============

lk08 / Ogl;{of larsf] ;DaGw -Relation between mass and inertia_

ljm| ofsnfk 7.8

bO' c{ f6] f Psgf;} aft] n dWo] Pp6fdf kfgL egx{' f;] \ / csf{n] fO{ vfnL /fVgx' f];\ . bj' n} fO{
;dfg nDafO ePsf] 8f]/Ln] cuf8L k5f8L kl] /of]l8s ¿kdf rNg ;Sg] u/L s'g} cf8df
em' 08o\ fpg'xf];\ . ca e'm08o\ fOPsf af]tnx¿nfO{ a/fa/ b/' L ;Dd lj:yflkt u/L;“u}
5f8] g\ x' f];\ / ltgLx¿sf] cfl] ;n]6/L rfnsf] cjnf]sg ugx'{ f;] \ . s'g j:t' klxn] l:y/
cj:yfdf cfp5“ < glthf x]/L To;sf] JofVof ug'{xf;] \ .

cjnfs] g glthf JofVof

sd lk08 ePsfnfO{ /f]lsg nfu]sf] ;do Ö === === eGbf ==== klxn]
a9L lk08 ePsfnfO{ /fl] sg nfu]sf] ;do Ö ==== /fl] sG5 .

110 lj1fg tyf kl| jlwM sIff (

sd lk08 ePsf] tyf a9L lk08 ePsf] bj' } j:t' oyfl:yltdf /xg vf]H5g\ . tL j:t'x¿df
afxo\ ansf] cj/fw] ug{] Ifdtf eg] km/s–km/s xG' 5 . t;y{ ;a} j:td' f Ogl;o{ f x'G5 . j:t'df
x'g] Ogl;{of o;sf] lk08df lge{/ x'G5 . j:ts' f] lk08 a9\bf Ogl;o{ f klg a9\5 / lk08 36b\ f
Ogl;{of klg 36\5 .

Ogl;o{ fsf lsl;d -Types of inertia_

!= l:y/ Ogl;o{ f -Inertia of rest_

lj|mofsnfk 7.9

Pp6 sfFrsf] lunf;, sf8{ / l;Ssf lng'xf;] \ . lrqdf h:t}
lunf;sf] dfly sf8{ / To;sf] dfly l;Ssf /fVgx' f];\ . ca
sf8{nfO{ PSsf;L tfGbf s] xG' 5, cjnf]sg ug'{xf;] \ . l:y/
cj:yfdf /x]sf] l;SsfnfO{ PSsfl; rfndf Nofpg vf]Hbf
o;n] To;sf] cj/fw] u5{ . sf8{ PSsf;L rfndf cfPsf]
xg' fn] l;Ssf rNg gkfpbF } of] l;Ssfaf6 6f9f hfG5 . h;n]
ubf{ l;Ssf lunf;df v:5 .

s'g} l:y/ cj:yfdf /xs] f] j:ts' f] l:y/ cj:yfd} /lx/xg lrq 7.19

vfH] g] u'0f l:y/ Ogl;o{ f xf] . dflysf] ljm| ofsnfkdf l;Ssfsf] l:y/ Ogl;o{ fn] ubf{ of]

sf8;{ Fu rfndf guO lunf;df v:5 . tn l:y/ Ogl;o{ fsf yk pbfx/0fx¿ k|:t't ul/Psf

5g\ .

i. ko| fu] df /xs] f] sfk{]6df lxsf{pbF f o;df ePsf] w'nf] em5{ .

ii. l:y/ cj:yfdf /xs] f] ;jf/L ;fwg h:t} a;nfO{ PSsf;L rfndf NofpFbf ofqx' ¿sf] z/L/
k5fl8 lt/ x'lQG5 .

iii. ?vdf cfFk kmn]sf] cj:yfdf o;sf] xfuF f xNnfpbF f cfkF v:5g\ .

iv. Sof/d vN] bf uf6] Lx¿sf] rfªdf l:6fOs/n] hf8] n] lxsf{Pdf s]an lkwF sf] uf6] L lg:sG5 /
afFsL rfFª g9nLsg a:5 .

dflysf pbfx/0fx¿df c;Gtl' nt ansf] c;/n] j:t' jf o;sf] efu l:y/ cj:yfaf6 rfn
cj:yfdf cfpFbf pSt kl/jt{gsf] cj/f]w ePsf] 5 . pbfx/0fsf nflu a; PSsf;L rfndf
cfpbF f To; leq /xs] f ofqx' ¿sf] z/L/sf] dflyNnf] efu l:y/ cj:yfd} /xg vfH] 5 t/
a;sf] ;Dksd{ f /x]sf] z/L/sf] tNnf] efu eg] a;;uF } rfndf cfpF5 . h;n] ubf{ ofq'x¿
k5fl8lt/ xl' QG5g\ .

lj1fg tyf kl| jlwM sIff ( 111

lj|mofsnfk 7.10

sIffdf 5nkmnsf] lgisifa{ f6 dfly lbOPsf pbfx/0fx¿df pTkGg x'g] Ogl;{ofnfO{ tnsf]
tflnsfcg';f/ JofVof ug'x{ f;] \ .

pbfx/0f rfndf cfpg] efu jf l:y/ cj:yfdf /xg l:y/ Ogl;{ofsf]

j:t' vf]Hg] efu jf j:t' JofVof

============= =================== ====================== ==========================

@= rfn Ogl;{of -Inertia of motion_

;uF+ s} f] lrqdf u8' b\ } u/s] f] ;fOsnsf] cufl8sf] kfªu\ |f Pp6f 7'nf] 9'ªu\ f;uF 7fl] sPsf]
b]vfOPsf] 5 . o;n] ;fOsnsf] ultnfO{ /f]S5 / of] l:y/ cj:yfdf cfpg vf]H5 . ;fOsn
rfnssf] z/L/ eg] klxn]s} ultn] cuf8L uO/xg vfH] 5 . h;n] ubf{ rfns cufl8 lt/
x'lQG5 / e'OF df k5fl/G5 . rfn cj:yfdf /xs] f] j:ts' f] ;dfg ultn] pxL lbzfdf rfn
cj:yfd} /lx/xg vf]Hg] u0' f rfn Ogl;o{ f xf] . tn rfn Ogl;o{ fsf yk pbfx/0fx¿ k:| t't
ul/Psf 5g\ .

i. rfnsn] ul' 8/xs] f] ;fOsnsf] k8] ndf an gnufpbF f klg sx] L ;do;Dd ul' 8/xG5 .

i. ul' 8/xs] f ;jf/L ;fwgx¿ h:t} a;df PSsfl; as]| nufpbF f o;df ePsf ofqx' ¿sf]
z/L/ cufl8lt/ x'lQG5 .

iii. 8f« Oe/n] 3D' tLx¿df a; PSsfl; df]8\bf ofqx' ¿sf] z/L/ a; df]8s] f] ljk/Lt lbzflt/
9lNsG5 .

iv. u'8b\ } u/s] f] a;af6 embf{ ofq' e'OFdf k5fl/g] ;Defjgf x'G5 .

v. nªu\ hDksf v]nf8Lx¿n] nfdf] 5nfª nufpg sx] L b'/L bu'g{] u5g{ \ .

ljm| ofsnfk 7.11

sIffdf 5nkmnsf] lgisifa{ f6 dfly lbOPsf pbfx/0fx¿df pTkGg x'g] Ogl;{ofnfO{ tnsf]
tflnsfcg;' f/ JofVof ug{x' f;] \ .

pbfx/0f l:y/ cj:yfdf rfn cj:yfd} /xg rfn Ogl;o{ fsf]
cfpg] efu jf j:t' vf]Hg] efu jf j:t' JofVof

================== ================== ====================== ============================

112 lj1fg tyf kl| jlwM sIff (

Go6' gsf] rfn;DaGwL klxnf] lgod -Newton's first law of motion_

lj|mofsnfk 7.12

5nkmnaf6 tnsf pbfx/0fx¿ h:t} bl} gs ljm| ofsnfkx¿df j:ts' f] cj:yf kl/jtg{ ug{ afx\o
kl/0ffTds ansf] cfjZostf pNn]v ug{x' f];\ .

klxnf] v08 -l:y/af6 rfn_ bf;] f| ] v08 -lbzf kl/jtg{ _ t;] |f] v08 -rfnaf6 l:y/_

!= db} fgdf vn] f8Lx¿n] k'm6an kf; ub}{ v]Nbf

klxnf] vn] f8Lsf] uf]8fn] k|xf/ klxnf] vn] f8Ln] nufPsf] olb km' 6an / hldglar
ubf{ nfUg] kl/0ffTds ann] pSt ansf] lbzfdf km' 6an l;wf 3if{0f an pTkGg gePdf
ansf] lbzfdf k'm6an u8' \5 . u'8/] hfG5 . csf]{ v]nf8Ln] k'm6an lg/Gt/ u'8Y\ of], h'g

nufPsf] kl/0ffTds ann] c;Dej xG' 5 . o;/L 3if0{ f
o;sf] lbzf kl/jt{g x'G5 . tyf cGo vn] f8Ln] nufpg]

kl/0ffTds afxo\ ann]
km' 6an l:y/ cj:yfdf
cfpF5 .

@= afª\uf]l6ª\uf] af6fdf a; u'8fpFbf

OGhLgn] nufpg] kl/0ffTds :6l] /ª lXjn -steering wheel_ a|s] tyf hldgl;tsf]
ansf] c;/ n] nfupg] kl/0ffTds ansf] 3if0{ fn] nfUg] kl/0ffTds
c;/ ansf] c;/
=====================
================================ =================================

Go'6gn] rfn ;DaGwL lgodx¿ k|ltkfbg ug'k{ "j{ j1} flgs Uoflnlnof] UoflnnL -Galileo Galilei_
n] rfn;DaGwL Jojl:yt ?kn] cWoog u/L Ogl;{ofsf] lgod lbO ;ss] f lyP . Go'6gn]
klg Ogl;o{ fnfO{ kl/eflift ub}{ rfn ;DaGwL klxnf] lgod kl| tkfbg u/]sf lyP . Go'6gsf]
rfn;DaGwL klxnf] lgodcg;' f/ …s'g} c;Gt'lnt ansf] ko| fu] gx'Gh]n ;Dd l:y/ cj:yfdf
/x]sf] j:t' l:y/ cj:yfd} /xG5 / rfn cj:yfdf ePsf] j:t' ;dfg ultn] pxL lbzfdf rfn
cj:yfd} /lx/xG5 . o; lgodcg';f/ olb kl/0ffTds an -resultant force_ zG" o ePdf j:t'
oyfl:ytLdf /xG5 . l:y/ cj:yfaf6 rfndf Nofpg / ;dfg ultn] u'l8/xs] f] j:tn' fO{ l:y/
cj:yfdf Nofpg c;Gtl' nt an nfUgk' 5{ . t;y{ Go6' gsf] rfn ;DaGwL klxnf] lgodn] ansf]
kl/efiff lbG5 . o; lgodn] c;Gtl' nt an gnfuG' hn] l:y/ cj:yfdf /x]sf] j:t' l:y/ cj:yfd}
/xg vf]Hg] / rfn cj:yfdf /x]sf] j:t' rfn cj:yfd} /xg vf]Hg] u'0faf/] pNnv] ug]{ ePsfn]

o;nfO{ Ogl;{ofsf] lgod -law of inertia_ klg elgG5 .

lj1fg tyf kl| jlwM sIff ( 113

rfn ;DaGwL Go'6gsf] bf;] |f] lgod (Newton's second law of motion)

5nkmnsf] k|Zg M ;fOsnnfO{ l:y/ cj:yfaf6 rnfP/ ult kl/jt{g ub}{ rfF8fr] f8F f] u'8fpg'kg]{
cj:yfdf PSn} rfns / rfnssf] k5f8L csf]{ JolSt a:bf k|ju] df s:tf] leGgtf cfpF5 <
;Dd k/]sf] Psgf;sf] af6f]df klxnf] k6s ;fOsnsf] k8] ndf sd an nufP/ u8' fpbF f / bf;] |f]
k6s k]8ndf a9L an nufP/ u'8fpbF f pTkGg xg' ] k|j]udf s] leGgtf xG' 5 <

rfnsn] nufpg] an l:y/

ePdf, lk08 a9b\ f kj| u]

36\5 . olb lk08 l:y/

ePsf] cj:yfdf ;fOsn

rfnsn] an a9fpg ;s]df

kj| ]u klg a95\ .

lrq 7.20 ;fOsn rfns dfq xb'“ fsf] lrq 7.21 ;fOsn rfns;u“ }
k|ju] k5fl8 csf{] JolSt af]Sbfsf] kj| u]

dflysf] k|Zgdf ;f]lwP h:t} b}lgs hLjgdf nfu' x'g] yk pbfx/0fx¿af/] 5nkmn ug{'xf;] \ .

j:t'sf] lk08df xg' ] kl/jt{gn] ubf{ j:t'df nufOPsf] ansf] 36a9n] kj| u] klg

kj| u] df klg kl/jt{g x'g] 36a9 xg' ]

xfdLn] afs] ]sf] ef/L la;fP/ l/Q} lxF8\bf rf8F f] dfz+ kz] Laf6 an a9L nufpFbf Ps} l5gdf

rfF8f] lx8F g\ ;lsG5 . tLj| ultn] bug' { ;lsG5 .

psfnfdf u8' b\ } u/]sf] 6«ssf] nf8] 36fpFbf ult ;jf/L ;fwgx¿df PS;n/]6/af6 OlGhgn]

kl/jt{g rfF8f] rf8F f] x'G5 . nufpg] an a9fpFbf kj| u] pTkGg x'G5 /

;fdfg nf8] ul/Psf] 7]nfuf8fnfO{ u'8fpg hf8] n] a]s| lyRbf tLj| ultx|f; x'G5 .

eGbf vfnL 7n] fuf8fnfO{ u8' fpg ;lhnf] xG' 5 . v]n d}bfgdf annfO{ rf8F f] rfF8f] u8' fpg a9L

an kof]u ug{'k5{ .

dflysf pbfx/0fx¿df j:t'sf] lk08df x'g] kl/jtg{ tyf pSt j:td' f nfufOPsf] andf xg' ]
kl/jt{gn] j:ts' f] kj| ]udf kg{] c;/ b]vfOPsf] 5 . an / lk08;Fu kj| ]usf] ;DaGw cWoog ug{
tnsf] ljm| ofsnfk u/f}F .

lj|mofsnfk 7.13

Pp6f 8foglds 6n« L jf To:t} vfnsf] 6fo] uf8L lng'xf;] \ . lrq 7.22 8fOgflds 6«nL
o;sf] ljsNkdf k]lG;nsf] tftF L dfly Hofldlt aS; /fvL
6«nLsf] gd'gf tof/ kfg{ ;lsG5 . pSt 6«nLnfO{ 6a] 'ndfly
/fVgx' f];\ . 6n« LnfO{ u'8fpg lrqdf e}Fm Ps 5]pdf lk08 yKg

114 lj1fg tyf k|ljlwM sIff (

ldNg] u/L em' 08\ofOPsf] lk08;Fu wfufn] ] afWF g'xf];\ . lk08 ;lhn} tnlt/ ;gs{ f nflu 6a] nsf]

5p] df l3gL{ jf 3'Dg ;Sg] j:t'sf] dfyL wfuf] /fVg'xf];\ . lk08 a9fpgsf nflu 50 u|fdsf
lk08x¿ klg lng'xf;] \ . 6n« LnfO{ u8' fpbF } tnsf] tflnsfdf lbOPsf tYofªs\ ;ª\sng ug' {xf];\ .
6«nL :yfgfGt/0fsf jm| ddf nfUg] ;do lx;fa ug{ :6k jfrsf] k|ofu] ug{x' f;] \ .

6«nLsf] lk08 l:y/ /fvL tfGg] an kl/jtg{ ubf{ tfGg] an l:y/ /fvL 6n« Ldf ePsf] lk08
kl/jt{g ubf{

tf}n :yfgfGt/0f ;do k|j]u lk08 :yfgfGt/0f ;do kj| ]u

(W) (s) (t) a= 2s (m) (s) (t) a= 2s
t2 t2

========= ============= ======= ============= ========= ============= ======= =============
========= ============= =======
============= ========= ============= ======= =============

tYofªs\ ljZni] f0f / glthf M tYofª\s ljZn]if0f / glthf M
an / kj| ]usf] lbzf M an / kj| ]usf] lbzf M

Go6' gsf] rfn;DaGwL bf];|f] lgodcg;' f/ …ansf] k|ofu] af6 s'g} j:td' f pTkGg xg' ] kj| u] To;df
nfus] f] an;uF ;dfg'kflts / To;sf] lk08;Fu Jo'Tjm| dfgk' flts xG' 5 .Ú

cyft{ ,\

sg' } j:td' f nfu]sf] kl/0ffTds an a9fpbF f To;df pTkGg x'g] kj| ]u klg a95\ .

k|j]u (a)∞F………………….( i) -lk08 l:y/ xbF' f_

j:t'df nfus] f] kl/0ffTds an l:y/ ePsf] cj:yfdf o;sf] lk08 a9b\ } hfFbf k|ju] 365\ / lk08
36b\ f k|j]u a9\5 .

k|ju] (a) ∞ 1/m………………..(ii) -an l:y/ xbF' f_

dflysf ;dLs/0f -i_ / -ii_ nfO{ ;+of]hg ubf{,

a ∞ F/m
F ∞ ma

s'g} ;DaGwnfO{ ;dLs/0fsf] ?k lbgsf nflu To;df Ps cr/ /fzL k|lji6 ug'{k5{ .

F = k ma……………..(iii) oxfF ko| fu] ePsf] k cr/ /flz xf] .
1 N ansf] kl/efiffcg;' f/, sg' } 1 kg lk08 ePsf] j:t'df 1 m/s2 sf] kj| u] pTkGg u/fpg
ko| f]u x'g] annfO{ 1 N elgG5 . ansf] dfg 1 N xb'F f ;dLs/0f (iii) df k sf] dfg klg 1 x'G5 .

\ F = ma

lj1fg tyf k|ljlwM sIff ( 115

pbfx/0f 7.5

Pp6f 1500 kg lk08 ePsf] sf/ pQ/ lbzfdf 36 km/h sf] ultn] u'l8/xs] f] lyof] . rfnsn]
o;sf] PS;n/]6/ lyRbf 4 s kl5 ;dfg kj| u] n] 64 m k/ kU' of] . pSt sf/df nfus] f] kl/0ffTds
an lx;fa ugx{' f;] \ . sf/df pTkGg k|ju] sf] lbzf pNn]v ugx{' f;] \ .

pbfx/0fdf lbOPsf]

sf/sf] lk08 (m) = 1500 kg

s f/sf ] ;'?s f] ult (u) = 36 km/h = 36 ×1000m = 10 m/s
60 × 60s

sf/sf] :yfgfGt/0f (s) = 64 m

:yfgfGt/0fsf nflu nfu]sf] ;do (t) = 4 s

l;wf /]vLo rfnsf] ;dLs/0f k|of]u ubf,{ lrq 7.23

s = ut + 1 at2
2

64 = 10 × 4 + 1 × a × 42
2

64 – 40 = 1 × a × 16
2

8a = 24

∴ a = 3 m/s2

Go'6gsf] rfn;DaGwL bf];|f] lgod k|ofu] ubf,{ sf/df nfu]sf] kl/0ffTds an

F=ma

F =1500 × 3 = 4500 N

t;y{ sf/df 4 s ;dfg kj| ]u pTkGg x'bF f nfus] f] kl/0ffTds an 4500 N /x5] . sf/df
pTkGg k|ju] sf] lbzf an nfus] f] lbzftkm{ x'G5 .

rfn;DaGwL Go6' gsf] t;] f| ] lgod (Newton's third law of motion)
kZ| g M s] lx8F b\ f xfdf| ] k}tnfn] hldgdf tnlt/ gbafOsg cufl8 a9\g ;S5f}F < Ps k6s sf]lz;
u/L xg] {x' f];\ .
5nkmn u/L nV] g'xf;] \ .
xfd|f] jl/kl/ cjnfs] g ug{ ;lsg] j:t'nfO{ rfndf Nofpg ul/g] lj|mofsnfkx¿df ljm| of /
kl| tlj|mof 5§' ofpg'xf;] \ .

116 lj1fg tyf kl| jlwM sIff (

pbfx/0f lrqdf lj|mof k|ltlj|mof

8ª' \uf 8ª' \uf rfnsn] 8ª' u\ f rfnsn] nufPsf]
lvofpbF f ug{] lj|mof axfgfn] an af/a/sf] an kfgLn]
an nufP/ kfgLnfO{ nufpF5 / 8ª' u\ f cufl8
k5fl8 ws]Ng] wsl] nG5 .

kfgLdf kf}8L kf}8L vN] g]n] kf}8L v]Ng]n] nufPsf]
v]Nbf ug{] lj|mof– xftn] ansf] a/fa/sf] an
an nufP/ kfgLnfO{ kfgLn] xftdf nufpF5 /
k5fl8 ws]Ng] . z/L/ cufl8 xl' QG5 .

annfO{ ========================== =======================
eF'Odf pkmfbf{

lrq 7.24

sg' } Ps j:tn' ] bf];f| ] j:t'df an nufpFbf bf];|f] j:t'n] klg klxnf] j:t'df ;fx] L dfg a/fa/ t/
l7s ljkl/t lbzdf an nufp5F . o;/L b'O{ j:tx' ¿df nfUg] hf8] L anx¿dWo] Pp6fnfO{ lj|mof
-action_ / csf]n{ fO{ k|ltlj|mof -reaction_ elgG5 . Go'6gsf] rfn ;DaGwL t];f| ] lgodcg;' f/
…sg' } klg lj|mofsf nflu a/fa/ / ljkl/t kl| tlj|mof xG' 5 .Ú

lj|mofsnfk 7.14

j:tn' fO{ rfndf Nofpb“ f x'g] ljm| of / kl| tljm| of ;DaGwL Pp6f >JobZ[ o ;fdu|L jf lrqx¿;lxtsf]
rf6{ cjnfs] g ug{'xf];\ . cfkm" n] cjnf]sg u/]sf] ;fduL| sf cfwf/df ljm| of / k|ltlj|mofsf] ;dx"
5'§ofpg'xf;] \ .

lrq 7.25

lj1fg tyf k|ljlwM sIff ( 117

lj|mofsnfk 7.15

b'O{cf]6f Psgf;sf l:kª| t/fh'x¿ lngx' f];\ . tn lrqdf bv] fOP h:t} l:kª| \ t/fh' B sf] Pp6f
5]pnfO{ c8\ofP/ /fVg'xf;] \ / csf{] 5p] sf] c+s'zd] f l:kª| t/fh' A sf] cs+ z' ] /fVgx' f;] \ . l:k|ª
t/fh' A sf] csf]{ 5]paf6 lj:tf/} an nufP/ aflx/ lt/ tfGgx' f;] \ . l:kª| t/fh' A / l:k|ª
t/fh' B n] bv] fpg] ansf] dfg / lbzf cjnf]sg ugx{' f;] \ .

lrqdf cjnfs] g glthf

l:k|ª t/fh' A n] l:kª| t/fh' B

df nufPsf] an Ö

l:kª| t/fh' B n] l:k|ª t/fh' A
df nufPsf] an Ö

lrq 7.26 Pp6 l:kª| t/fhn' ] csf{n] fO{ tfgs] f

lj|mof / kl| tljm| of bj' } slxNo} klg Pp6} lrq 7.16 lbO' { cf]6f anx? Ps cfk;df 7f]
j:td' f nfUb}gg\ . Go'6gsf] rfn;DaGwL lsbf Pp6fn] csfd]{ f nufpg] an
lgodcg';f/ s'g} j:t' A n] j:t' B df an
nufof] eg] j:t' B n] klg j:t' A df plQg}
dfqfdf ljk/Lt lbzfdf an nufpF5 .

lj|mof / kl| tlj|mofdf a/fa/ kl/df0f / lrq 7.27 lrq 7.28
ljkl/t lbzf eP tf klg Psn] csfn{ fO{
/2 ub}g{ . ha bO' { a/fa/ / ljk/Lt an
Pp6} j:td' f nfUb5g\ ta dfq kl/0ffTds
an -resultant force_ z"Go x'G5 . lj|mof /
k|ltljm| of b'O{ km/s ;txdf nfUg] ub{5g\ .
To;}n] lj|mof / k|ltlj|mofdf Psn] csf{nfO{
/2 ug{] x'bF g} .

ljm| ofsnfk 7.16

Pp6f an] g' lng'xf;] \ . o;sf] ;txdf :6« kfOk jf lrq 7.29 a]n'gsf] /s6]
sfuhsf] gnL h:tf] agfP/ lrqdf e“}m 6f:“ g'xf;] \ .
pSt gnL leq dl;gf] 8f/] L /fv/] b'Oc{ f6] } 5]pnfO{
s'g} cf8df af“Wgx' f;] \ . an] g' df xfjf eg'x{ f;] \ / o;sf]
d'v xftn] RofKg'xf;] \ . ca a]n'gsf] d'v PSsf;L
5f8] g\ x' f];\ / Go6' gsf] rfn;DaGwL t;] |f] lgodsf
cfwf/df o;sf] rfnsf] j0f{g ugx{' f];\ .

118 lj1fg tyf kl| jlwM sIff (

Onfl:6l;6L / Knfl:6l;6L

tkfOnF ] Onfl:6s zAb k9\bf o;;Fu ;DaGwLt s'g–s'g j:t' ;lDemg' x'G5 < To:t}, Knfl:6s
eGgfn] s'g–s'g j:t' ;Demg' x'G5 < ;r" L agfpg'xf;] \ . tnsf] lj|mofsnfksf] lg:sif{ / lzIfssf]
;xof]udf cfkm" n] tof/ kf/]sf] ;"rL ef}lts lj1fgsf] kl/efiffcg';f/ ldn] gldn]sf] hfFRgx' f;] \ .

lj|mofsnfk 7.17

ansf] c;/

an nufp“bf ug{'kg{] ljm| of lrqdf cfsf/÷;fOhdf an x6fpb“ f kg' M dn"

kl/jt{g cj:yfdf cfpg] ÷gcfpg]

d]6\g] /a/sf bO' { ============== cfpg]
5p] af6 RofKg], cfsf/ kl/jtg{ =============
tGsfpg,] aªU\ ofpg], ===================== ========================
a6fg{]
==================== =========================
/a/ a]G8 tGsfpg] ===============

xftsf cfnF} fn] 6'y k]:6 =================
RofKg]

Ps 5p] RoflkPsf] =================
kfl] nlyg emf]nfsf] csf]{
5p] af6 tfGg]

xfjf e/]sf] a]ng' nfO{ =================
bO' { xftsf] lardf /fvL
lyRg]

7f8f] kfl/ /flvPsf] ===================
l:6n l:kª| nfO{ lj:tf/}
lyRg÷] tfGg]

/a/ AofG8nfO{ lj:tf/} tfGbf o;sf] nDafO a95\ . o;df nufOPsf] afxo\ an x6fpbF f of] cfˆgf]
d"n nDafOdf lkmtf{ cfpbF 5 . To:t} Pp6f /a/sf] an jf el/Psf] a]ng' lyRbf cfsf/ kl/jtg{
x'G5 / afXo an x6fpFbf kg' M cfkm\ gf] jf:tljs cfsf/ kf| Kt ub{5 . s'g} j:t'df ljleGg lbzfaf6
an nufpbF f ;dud| f Psn ansf] ?kdf kl/0ffTds an -resultant force_ sf] c;/ bl] vG5 .
j:ts' f] agfj6, nufOPsf anx¿sf] kl/df0f tyf lbzfcg';f/ kl/0ffTds ann] j:ts' f] cfsf/
/ ;fOh kl/jt{g ug{ ;S5 . kl/0ffTds an h;n] j:t'sf] cfsf/ / ;fOhdf kl/jtg{ NofpF5

To;nfO{ l8kmld{ª an -deforming force_ elgG5 .

k|Zg M s] l:6n l:kª| nfO{ hlt ;Sbf] tGsfP kl5 k'gM d"n l:yltdf lkmtf{ cfp5“ xfn] f <

sg' } lglZrt ;Ldf;Dd l8kmdD{ 8 j:t' -deformed body_ af6 l8kmld{ª an x6fpFbf pSt j:t'

lj1fg tyf kl| jlwM sIff ( 119

cfˆgf] dn" l:yltdf lkmtf{ cfpF5 . l8kmd{D8 j:t' leq ljsl;t l/:6fl] /ª\ an -restoring force_
sf] sf/0fn] To;n] cfˆgf] dn" cj:yf lkmtf{ lng ;Sb5 . s'g} l8kmdD{ 8 j:t'af6 l8kmldª{
annfO{ x6fpbF f cfk\mgf] d"n cj:yf kf| Kt ug{] u0' f Onfl:6l;6L xf] .

agfj6sf cfwf/df j:tx' ¿df km/s km/s Onfl:6l;6L lrq 7.30 Ps vDafdf cl8P/
xG' 5 . Onfl:6l;6L a9L x'g] j:t'n] l8kmld{ª ansf] /8x¿n] yfldPsf] s0ffn{ L kn'
a9L cj/fw] ub{5 / pSt an x6fpFbf Psbd} rf8F f]
oyfl:yltdf kmsG{ 5 . l:6nsf] Onfl:6l;6L Psbd} a9L
x'g] ePsf o;sf] k|of]u alnof] 3/, kn' , cflb lgdf0{ fsf
nflu ul/G5 . Onfl:6l;6L xg' ] j:t'x¿sf] k|ofu] ubf{
lglZrt ansf] k|of]u ug{'k5{ . j:tn' fO{ Onfl:6l;6L
;LdfeGbf a9L tGsfpbF f pSt j:t' :yfoL ?kdf l8kmd{D8
xG' 5 / Onfl:6l;6L x/fp5F . o;/L ansf] ko| f]un] j:t'sf]
cfsf/ / ;fOhdf :yfoL ?kn] kl/jtg{ cfpg] u'0fnfO{
Knfl:6;L6L elgG5 . Knfl:6l;6Ln] ubf{ df6fn] fO{ ;lhn}
cfsf/ lbP/ OF6f agfpg ;lsG5 . :yfoL ?kn] l8kmd{D8
j:td' f lg/Gt/ an a9fpFbf rFl' 8g] jf eflrg] xG' 5 .

lrq 7.31

5nkmn ugx'{ f];\ M
!= s] an nufpFbf tlGsPsf] b]lvg] j:t'x¿ dfq Onfl:6s x'g\ <
@= Onfl:6s j:ts' f u0' fsf cfwf/df /a/ / l:6ndWo] s'g a9L Onfl:6s xG' 5 <

kl/ofh] gf sfo{

-s_ cfkm\ gf] jl/kl/ pknAw ;fdu|Lx¿sf] ko| fu] u/L an] 'gaf6 rNg] 6f]o sf/ lgdf{0f ugx{' f;] \ .
pSt sf/df km/s km/s Onfl:6l;6L ePsf u'Aaf/f / ljleGg tfn} x¿sf] k|ofu] af6 Go'6gsf]
rfn ;DaGwL bf;] f| ] lgod k|bzg{ ug'{xf];\ .

120 lj1fg tyf kl| jlwM sIff (

-v_ :yfgLo ?kdf pknAw ;fdu|Lx¿ / /a/ a]G8sf] Onfl:6l;6Lsf] k|ofu] u/L Pp6f 6fo]
xl] nsf]K6/ lgdf{0f ugx'{ f;] \ .

k|ltljDjg

!= :yfgfGt/0f ;do uf| km / ult ;do uf| kmsf] t'ngfTds cWoog

uf| kmdf bv] fOP u|fkmdf bv] fOP

u|fkm e'msfjsf] x-cIf ;“u e}“m ems' fj em}“ em' sfj aqm /]vf
dfg ;dfgfGt/ ;lxtsf] l;wf ;lxtsf] l;wf

/v] f /v] f

:yfgfGt/0f– ult e'msfj z"Go, Psgf;sf] Psgf;sf] s'g} b'O{
;do /v] f j:t' l:y/ em' sfj, ;dfg e'msfj, ;dfg laGb'df
cj:yfdf ultn] cufl8 ultn] k5fl8 em' sfj
u l t – ; d o k|j]u km/s– km/s,
/v] f e'msfj zG" o, Psgf;sf] Psgf;sf] c;dfg ult
;dfg ult em' sfj, ;dfg em' sfj, ;dfg
k|j]u ultxf| ; sg' } b'O{
laGbd' f
e'msfj
km/s– km/s,
c;dfg kj| u]

@= l;wf /]vLo rfn;DaGwL ul0ftLo ;d:of ;dfwfgsf nflu pko'St ;dLs/0fsf] 5gf6]

yfxf xg' 'kg]{ r/ /fzLx¿ t];f]{ rfnsf nflu ;dLs/0f 7f8f] rfnsf nflu ;dLs/0f

;'?sf] ult -u_, clGtd ult v = u + at v = u + gt
-v_, k|ju] -a_ / ;do -t_ dWo]
s'g} tLg cf]6f v2 = u2+ 2as v2 = u2 + 2gh

;?' sf] ult -u_, clGtd ult
-v_, kj| ]u -a_ / :yfgfGt/0f -s_
dWo] s'g} tLg cf]6f

lj1fg tyf k|ljlwM sIff ( 121

;'?sf] ult -u_, kj| ]u -a_ / 1 1
2 2
;do -t_ / :yfgfGt/0f -s_ dWo] s = ut + at2 h = ut + gt2
s'g} tLg cf]6f

#= rfn;DaGwL Go6' gsf lgodx¿

klxnf] lgod bf];f| ] lgod t;] f| ] lgod

sg' } c;Gtl' nt ansf] k|of]u gx'Gh]n ansf] ko| fu] af6 s'g} j:t'df s'g} klg lj|mofsf
;Dd l:y/ cj:yfdf /xs] f] j:t' l:y/ pTkGg x'g] k|j]u To;df nfus] f] nflu a/fa/ /

cj:yf d} /xG5 / rfn cj:yfdf an;uF ;dfgk' flts / To;sf] ljkl/t k|ltlj|mof
ePsf] j:t' ;dfg ultn] pxL lbzfdf lk08;uF JoT' qmdfgk' flts x'G5 . xG' 5 .
rfn cj:yf d} /lx/xG5 .

$= Onfl:6l;6L / Knfl:6l;6L

u'0f l8kmldª{ an x6fpb“ f cfsf/df xg' ] l/:6fl] /ª an
kl/tg{ sf] lsl;d
Onfl:6l;6L klxn] s} cfsf/df cfpg] c:yfoL ljsl;t x'g]
Knfl:6l;6L kl/jlt{t cfsf/ oyfjt /xg] :yfoL ljsl;t gx'g]

cEof;

!= ;xL pQ/ 5fGg'xf;] \ .
-s_ ult—;do /v] fsf] e'msfjn] s] sf] dfg lbG5 <
-c_ j]u -cf_ ult
-O_ kj| u] -O_{ :yfgfGt/0f
-v_ lbOPsf] ult ;do u|fkm;u+F ;DaGwLt :yfgfGt/0f ;do uf| km sg' xf] <

122 lj1fg tyf kl| jlwM sIff (

-u_ u8' \b} u/]sf] a;af6 cfn] g{ ' hf]lvdk0" f{ x'G5 . o; egfO{nfO{ sg' cfwf/df kl' i6 ug{
;lsG5 <
-c_ l:y/ Ogl;{of -cf_ rfn Ogl;o{ f
-O_ rfn ;DaGwL bf;] f| ] lgod -O{_ rfn;DaGwL t;] f| ] lgod
-3_ ljm| of / k|ltlj|mofsf ;Gbe{df s'g egfO ;xL x'G5 <
-c_ Psn] csfn{] fO{ /2 ug{ ;S5g\ .
-cf_ bj' } Pp6} ;txdf nfU5g\ .
-O_ a/fa/ t/ pxL lbzfdf nfU5g\ .
-O{_ b'O{ km/s km/s j:t'df nfU5g\ .
-ª_ Onfl:6l;6Lsf] k|ofu] sg' xf] <
-c_ df6fn] fO{ cfsf/ lbP/ udnfdf ?kfGt/0f ug'{
-cf_ kmnfdnfO{ lk6]/ kftf agfpg'
-O_ ldrs] f] lk7fn] fO{ /f]l6sf] cfsf/ lbg'
-O{_ Aofl6\dG6gsf] /s] 6] n] ss{ xfGg'
-r_ ;8sdf ;dfg ultn] u'l8/x]sf dfnafxs 6«s / sf/df ;dfg an
nufpg ;Sg] a|s] sf] ko| f]u u/L /fl] sPdf tnsf dWo] s'g egfO ;xL x'G5 <
-c_ 6«sn] kf/ ug{] b/' L sf/n] kf/ ug{] b/' L eGbf sd x'G5 .
-cf_ sf/n] kf/ ug]{ b'/L 6s« n] kf/ ug{] b'/L eGbf sd x'G5 .
-O_ 6s« n] kf/ ug]{ b/' L sf/n] kf/ ug{] b'/L ;dfg xG' 5 .
-O_{ 6s« n] kf/ ug]{ b/' L sf/n] kf/ ug{] b/' L ;u+ ;DaGwLt xF'b}g .
@= km/s nV] gx' f];\ .
-s_ :yfgfGt/0f ;do u|fkm / ult ;do uf| km
-v_ l:y/ Ogl;{of / rfn Ogl;o{ f
-u_ Onfl:6l;6L / Knfl:6l;6L

lj1fg tyf k|ljlwM sIff ( 123

#= sf/0f n]Vg'xf;] \ M

-s_ ;dfg ultn] ul' 8/xs] f df6] /;fOsn, sf/, 6«s, a;, 6]g« cflbnfO{ l:y/ cj:yfdf
Nofpg km/s km/s ;do nfU5 .

-v_ /Ltfn] xftn] l6Kg g;lsg] cfkF emfg{ xfuF fn] fO{ xNnfOg / 7n' f7n' f cfkF sf bfgfx¿
;lhn} v;] .

-u_ a; ofqfsf j|mddf ofq'n] cfkm\ gf] l;6;+Fu} eOF' df /fvs] f] emf]nf a; rns] f] sx] L ;do
kl5 cufl8sf] l;6 glhs ku' s] f] e6] ] .

-3_ aGbs' af6 ufn] L 5f8] b\ f o;nfO{ bl/nf] cf8 lbg'k5{ .

-ª_ bO' {cf6] f ;dfg cfsf/ ePsf /a/sf anx¿nfO{ ;+Fu} e'O{Fdf v;fNbf Pp6f a9L plkm| Psf]
kfOof] .

-r_ /a/ aG] 8nfO{ lglZrt ;LdfeGbf a9L tGsfpg' x'bF g} .

$= tnsf kZ| gx¿sf] pQ/ nV] gx' f];\ M

-s_ cf};t ult / k|j]usf] kl/efiff nV] g'xf;] \ M

-v_ lgDg l;wf /v] Lo rfnsf ;dLs/0fx¿ kd| fl0ft ug{'xf];\ .

-c_ v = u + at

-cf_ v2 = u2 + 2as

O_ s = ut + 21at2

-u_ l;wf /v] Lo rfndf ;dfg ultn] ul' 8/x]sf] j:ts' f] rfn b]vfpg Ps–Ps cf6] f
:yfgfGt/0f ;do u|fkm / ult ;do uf| km lrq sfg] x{' f;] \ .

-3_ lbOPsf] tYofª\ssf cfwf/df :yfgfGt/0f ;do u|fkm lvRgx' f];\ . pSt uf| kmdf
:yfgfGt/0f ;do /v] fsf] em' sfj cWoog u/L rfnsf] ks| l[ t pNnv] ug'{xf];\ .
em' sfjsf] cfwf/df rfndf /xs] f] j:ts' f] klxnf] 4 s sf] cf;} t ult lx;fa ugx{' f;] \ .

;do -s_ 0 24 68 10 12 14

:yfgfGt/0f -m_ 0 4 8 8 12 8 4 0

124 lj1fg tyf k|ljlwM sIff (

-ª_ ;u+F s} f] :yfgfGt/0f
;do u|fkmdf v/fof]
/ s5'jfsf] bf8} af/]
syfdf v/fof] /
s5j' fsf] rfnnfO{ Ps
l;wf /]vLo rfnsf
?kdf kb| zg{ ul/Psf]
5 . pSt u|fkmsf]
cjnf]sg u/L bf}8sf]
;?' cftb]vL clGtd
;Dd v/fof] / s5'jfsf] bf8} lj|mof ;dfjz] u/L syf n]Vg'xf;] \ .

-r_ Ogl;o{ f egs] f] s] xf] < l:y/ Ogl;o{ f / rfn Ogl;o{ fsf bO' { bO' c{ f6] f pbfx/0fx¿ nV] gx' f;] \ .

-5_ lk08 / Ogl;{of larsf] ;DaGw nV] g'xf];\ .

-h_ rfn;DaGwL Go'6gsf] klxnf] lgod n]Vg'xf];\ .

-em_ kl/0ffTds ann] j:t'sf] cj:yf abN5 egL b]vfpg b'O{cf]6f pbfx/0fx¿ n]Vg'xf];\ .

-`_ tLj| ult / Go6' gsf] rfn;DaGwL klxnf] lgodsf cfwf/df kxf8sf 3'DtLx¿df xg'
;Sg] a; b'3{6gfaf/] JofVof ug{x' f;] \ .

-6_ rfn;DaGwL Go6' gsf] bf;] |f] lgod nv] L kj| u] sf] lk08 / an;uF sf] ;DaGw F = ma
k|dfl0ft ug{x' f];\ .

-7_ rfn;DaGwL Go6' gsf] t;] |f] lgod n]Vg'xf];\ .

-8_ bl} gs hLjgdf Go6' gsf rfn;DaGwL tLgcf]6} lgoddf cfwfl/t ljm| ofsnfksf bO' {
bO' {cf]6f pbfx/0fx¿ nV] gx' f;] \ .

-9_ ljleGg ljm| ofsnfkdf Go'6gsf rfn;DaGwL klxnf] lgod, bf];f| ] lgod / t;] f| ]
lgodsf sg' } b'O{ b'Oc{ f]6f pkof]ux¿ vfh] L u/L ltgsf] JofVof ugx'{ f;] \ .

lj|mofsnfk pkof]u x'g] rfn;DaGwL AofVof
===================== Go6' gsf] lgod

==================== ========================

lj1fg tyf kl| jlwM sIff ( 125

-0f_ tn lrqdf b]vfOPsf lj|mofsnfkx¿df lj|mof / k|ltlj|mof 5'6\ofpgx' f;] \ .

-t_ pbfx/0f;lxt Onfl:6l;6L / Knfl:6l;6L kl/eflift ug{x' f];\ .

ul0ftLo ;d:ofx¿

-s_ l:y/ cj:yfaf6 wfjg dfud{ f blIf0f lbzf tkm{ u'8g\ ;?' u/s] f] xjfOhxfhdf 1.5 m/s2
sf] ;dfg kj| u] pTkGg eof] / 30 s kl5 hldgaf6 p8\of] . xjfOhxfh wfjgdfu{df u'8b\ f
;?' sf] :yfgaf6 clGtd :yfg ;Ddsf] :yfgfGt/0f / l7s hldgaf6 p8\g' k"js{ f] ult
lx;fa ug'{xf;] \ . (675 m blIf0f, 45 m/s blIf0f_

-v_ /fx] gn] Pp6f kn' sf] dfly af6 gbLsf] kfgLdf 9ª' \uf v;fn] / ;'/hn] tn glbsf] 5]pdf
a;L :6kjfrsf] ;xoftfn] 9'ª\ufnfO{ kfgLsf] ;tx;Dd cfOk'Ug nfu]sf] ;do 2 s kQf
nufP . 9ª' u\ fsf] v;fOdf kj| u] nfO{ 9.8 m/s2 dfgL kfgLsf] ;txaf6 kn' sf] prfO lx;fa
ug{'xf];\ . (19.6 m)

-u_ ;'/hsf] lk08 50 kg / pgn] r9s] f] ;fOsnsf] lk08 12 kg /xs] f] 5 . pgn] cf/] fnf]
af6f]df ;fOsn u8' fpFbf 2 m/s2 sf] kj| ]u pTkGg eof] . pSt cj:yfdf ;fOsndf nfu]sf]
kl/0ffTds an lx;fa ugx'{ f;] \ . (124N)

-3_ Pp6f 1500 kg lk08 ePsf] sf/ 72 km/h sf] ultn] u'l8/xs] f] lyof] . rfnsn] a|s] sf]

ko| fu] ubf{ 50 m sf] sf] ult 10 km/h eof] . pSt cjlwdf sf/df nfus] f] kl/0ffTds

an lx;fa ug{'xf];\ . (5850 N )

-ª_ ;uF }sf] lrqdf Pp6f a;sf] rfnnfO{ ult–;do uf| kmdf bv] fOPsf] 5 . uf| kmsf] cWoog u/L
tnsf kZ| gx¿sf] pQ/ nV] gx' f;] \ .

-c_ ;dfg ult, ;dfg kj| u] , c;dfg
k|j]u / ultx|f;sf v08x¿ 5'66\ ofP/
n]Vgx' f;] \ .

-cf_ ;dfg k|ju] ePsf v08x¿ dWo] s'g
v08df j:t'sf] ult tLj| ¿kn]
kl/jtg{ ePsf] /x]5 <

-O_ C / D sf] lardf a;sf] kj| u] slt 5 <

-O_{ a;n] C af6 D df k'Ubf xg' ] :yfgfGt/0f
lx;fa ugx'{ f];\ . -70 m k"j{_

126 lj1fg tyf kl| jlwM sIff (

* ;/n oGq
(Simple Machine)

lj|mofsnfk 8.1
tnsf lrqx¿ cjnf]sg u/L tflnsf k/" f ug'{xf;] \ M

;/n oGq
agfj6 /

sfo{

ul/Psf]
sfo{

ko| fu] ePsf]
;/n oGq

;/n
oGqsf]
agfj6

lrq 8.1

b}lgs hLjgdf ul/g] ljleGg lsl;dsf sfon{ fO{ ;xh agfpg w/] } ks| f/sf cf}hf/sf]
k|of]u ul/G5 . kr] s;, l3gL{, kfª\uf| / laF8, lrD6f, df6] / prfNg] Hofs, xFl;of, aGr/f] cflb
3/fo;L sfo{df ko| f]u xg' ] cfh} f/x¿ x'g\ . oL cfh} f/ k|of]u ug{ lah'nL, l8hn] jf k]6f« n] sf]
cfjZostf kbg{} . dfgjLo ann] dfq ;~rfng ug{ ;lsG5 . o;/L xfd|f sfo{nfO{ ;lhnf],
l56f] / ;'ljwfhgs 9ªu\ n] ;DkGg ug{ k|ofu] ul/g] ;fwf/0f agfj6 ePsf pks/0fnfO{ ;/n
oGq elgG5 . agfj6sf cfwf/df ;/n oGq 5 k|sf/sf xG' 5g\ . tL x'g,\ pQfn] s -lever_, l3gL{
-pulley_, kfª\u|f / la8F -wheel and axel_, 58s\ ] ;tx -inclined plane_, kr] -screw_ / km;] f]
-wedge_ .

lj1fg tyf kl| jlwM sIff ( 127

;/n oGqsf] ko| f]un] an j[l4 ug{ ;lsG5 . lrq 400 N
8.1 df pQf]nssf] k|ofu] u/L sfo{ ubf{ 400
N an nufP/ 600 N sf] nf]8nfO{ p7fOPsf] 600 N

5 . cyf{t nf]8 prfNg ko| f]u ePsf] ansf] 10 m

1 .5 (640000 N = 1.5) u0' ff a9L nf]8 p7fOPsf] 5m
N
lrq 8.2 pQf]nssf] ko| f]un] nf]8 prflnPsf]
5 . s'g} klg ;/n oGq ko| fu] u/L sfo{ ubf{

andf ePsf] lskmfotLnfO{ oflGqs kmfObf elgG5 .

ul0ftLo ¿kdf

oflGqs kmfObf (Mechanical Advantages- MA) = nf8] (Load)÷Okmf]{6 (Effort)

oflGqs kmfObf bO' c{ f]6f ansf] cgk' ft ePsfn] o;sf] s'g} PsfO xFb' g} . 10m = 2)
lrq 8.1 sf] pQfn] sdf ann] kf/ ug{] b'/L tfn} n] kf/ ug]{ b/' Lsf] 2 ( 5m
u'0ff

5 . o;n] pSt pQf]nssf] ult cg'kft lbG5 . sg' } klg ;/n oGqdf Okmf6{] ult (Velocity of

effort) / nf8] sf] ult (Velocity of load) sf] cg'kftnfO{ ;/n oGqsf] ult cgk' ft elgG5 .

ul0ftLo ¿kdf

ult cg'kft (Velocity Ratio - VR) = Okmf]{6 ult ÷ nf8] sf] ult

olb nf]8 / Okmf{6] n] lglZrt b/' L a/fa/ ;dodf kf/ u5{ eg],

ult cg'kft (VR) = Okmf6]{ n] kf/ u/]sf] b/' L / nf]8n] kf/ u/]sf] b/' L

= Okmf{]6 b'/L ÷ nf8] b'/L x'G5 .

ult cg'kft bO' c{ f6] f b/' Lsf] cgk' ft ePsfn] o;sf] s'g} PsfO xF'bg} .

dfly pNnv] ePsf ;q" x¿sf] k|of]uaf6 l3gL{, 58s\ ] ;tx, kfªu\ |f / la8F , km] ;f] / kr] sf nflu
klg oflGqs kmfObf, ult cg'kft kQf nufpg ;lsG5 .

1. l3gL{ (Pulley)

l3gLs{ f] ko| f]u gu/L emG8fT] fng ubf{ 8f/] Ldf nufOPsf] ansf] lbzf dflylt/ x'G5 t/ l3gL{sf]
k|of]u ubf{ an tnlt/ nufOG5 . oxfF l3gLn{ ] ansf] lbzf kl/jtg{ u//] sfdnfO{ ;lhnf]
agfOlbPsf] xG' 5 . l3gL{ Ps ks| f/sf] ;/n oGq xf] . cfˆgf] cIfdf :jtGq ¿kdf 3'Dg ;Sg]
sf7, Knfl:6s jf wft'af6 ags] f] ufn] f] rSsfnfO{ l3gL{ elgG5 . o;sf] kl/lwdf 8f/] L /fVg
vfN8f] agfOPsf] x'G5 . 8f/] Lsf] Ps 5p] df tf}n (load) /flvG5 eg] csf]{ 5p] df an -effort_
nufOG5 . l3gL{sf] k|of]u ljleGg 7fpFdf ul/G5, h:t} M Ogf/af6 kfgL tfGg, 7n' f 7'nf
ejgx¿ agfpFbf lgdf0{ f ;fduL| dflyNnf] tnfdf nh} fg cflb .

128 lj1fg tyf k|ljlwM sIff (

ljm| ofsnfk 8.2

lrqdf bv] fP h:t} u/L Ps rSs] crn

l3gL{, Ps rSs] rn l3gL{ / ;+oS' t

l3gL{ h8fg ug'{xf;] \ . sdfgL t/fh'

-spring balance_ sf] k|of]u u/L k|Tos]

l3gL{ k0| ffnLdf kfn}kfnf] lbPsf] nf8]

prfNgx' f;] \ . nf]8nfO{ 20 cm dfly

p7fpg Okmf] 6{nfO{ slt b'/L;Dd tfGg' crn l3gL{ rn l3gL{ ;+o'St l3gL{

k¥of] :sn] n] gfk]/ kQf nufpg'xf;] \ . lrq 8.3

o; lj|mofsnfkaf6 cfjZos tYofªs\ x¿ ;ª\sng u/L tnsf] h:t} tflnsfdf egx{' f;] \ .

tL tYofªs\ sf cfwf/df lx;fa ug'x{ f;] \ / ;fl] wPsf k|Zgx¿ xn ug'{xf;] \ .

gf]6 M Okmf]6{n] kf/ u/s] f] b/' L -effort distance_ eGgfn] 8f/] L ;?' sf] :yfgaf6 slt 6f9f k'Uof]
eGg] hgfp5F . nf]8n] kf/ u/s] f] b'/L -load distance_ eGgfn] nf]8 ;'?sf] cj:yfaf6 slt
dfly p7\of] eGg] hfgfp5F .

l3gL{sf nf]=b=' O=b=' O=b'=÷nf=] b'= Nff8] Okmf]6{ nf]8÷Okmf]6{ ul/Psf] sfo{ kf| Kt xg' ] sfo{ Ö
k|sf/ ÖOkmf6] { × O=b' nf8] × nf]=b'

-c_ klxnf] lrqdf bv] fOPsf] l3gL{ / bf];f| ] lrqdf b]vfOPsf] l3gLd{ f s] leGgtf 5 <

-cf_ Okmf]6{ b/' L / nf]8 b/' Lsf] cg'kft / l3gLs{ f] ;ª\Voflar s] ;DaGw 5 <

-O_ s'g l3gL{ ;dx" df nf]8 / Okmf]6s{ f] cg'kft ;a}eGbf sd / s'gdf ;a}eGbf a9L 5 <

-O_{ o:tf l3gL{x¿ s'g sg' 7fpdF f k|of]u u/s] f] bV] ge' Psf] 5 <

l3gL{ k0| ffnL crn, rn / ;+oS' t u/L tLg ks| f/sf xG' 5g . sg' } lglZrt 7fFpdf l:y/ /x]/ 3D' g]
l3gL{nfO{ crn l3gL{ elgG5 . o;nfO{ ansf] lbzf kl/jt{g ug{ ko| fu] ul/G5 . tf}n;uF } :yfg
kl/jtg{ xg' ] l3gLn{ fO{ rn l3gL{ elgG5 . rn l3gLn{ ] ansf] lbzf kl/jt{g ug{ ;Sb}g . rn
/ crn bj' } k|sf/sf rSsfx¿ ePsf] l3gLn{ fO{ ;o+ S' t l3gL{ elgG5 . ;o+ 'St l3gLd{ f sDtLdf
Pp6f rn / Pp6f crn rSsfx¿ x'G5g\ . rSsfx¿sf] ;ª\Vof a9fpbF } nh} fFbf l3gLn{ ] ug]{ sfd
j|mdzM sd ann] ug{ ;lsG5 . sd ann] w/] } sfd x'gn' fO{ lskmfotL xg' ' elgG5 . t;y{ w/] }
rSsf ePsf l3gL{x¿ a9L lskmfotL xG' 5g\ .

lj1fg tyf k|ljlwM sIff ( 129

ult cg'kft (Velocity ratio)

Psn rn l3gLd{ f nf]8n] kf/ ug]{ b/' LeGbf

Okmf]6n{ ] kf/ ug{] b/' L bf]Aa/ x'g] ePsfn]

ult cgk' ft 2 x'G5 . 3if{0f gu0o ePsf]

cj:yfdf o; l3gL{df xfdLn] nufPsf] an

b'O{ u'0ff k|jtg{ -magnify_ x'G5 t/ 3if0{ fn]

ubf{ ;/n oGqsf] oflGqs kmfObf ult lrq 8.4 Psn rn l3gLd{ f an b/' L / tfn} b/' L
cg'kfteGbf sd xG' 5 . ult cg'kftnfO{

3if{0fn] c;/ ub{}g t/ oflGqs kmfObfnfO{ eg] 3if{0fn] c;/ ub5{ .

lj|mofsnfk 8.2 af6 kf| Kt lgisifc{ g';f/ Ps rSs] crn l3gL{df nf8] n] kf/ ug{] b/' L / Okmf6] n{ ]
kf/ ug{] b'/L a/fa/ xg' ] ePsfn] ult cgk' ft 1 xG' 5 . l3gLd{ f ult cgk' ftsf] dfg l3gL{nfO{
yfDg k|of]u ePsf 8f/] Lsf bO' { v08sf] ;ªV\ of;uF a/fa/ x'G5 . t;y{

ult cg'kft (VR) = nf]8nfO{ yfDg k|of]u ul/g] 8f]/Lsf] v08sf] ;ªV\ of

Psn crn l3gLd{ f 3if{0f guGo ePdf nf]8 / Okmf]6{ a/fa/ x'G5 . t;y{ oflGqs kmfObf
;fdfGotof Ps xG' 5 t/ 3if{0fn] ubf{ l3gLd{ f nufpg] an tf}neGbf a9L xg' klg ;S5 . o:tf]
cj:yfdf o;sf] oflGqs kmfObf PseGbf sd x'G5 . oflGqs kmfObf Ps jf PseGbf sd eP
tfklg o;n] ansf] lbzf kl/jtg{ ub5{ . nf]8nfO{ ;fe] m} dfly prfNg'eGbf l3gL{ k|of]u u/L
annfO{ tnlt/ nufP/ nf8] dfly prfNg ;lhnf] xG' 5 .

oflGqs kmfObf (Mechanical Advantage)

ljm| ofsnfk 8.2 df nf]8 / Okmf]6{sf] cgk' ftn] oflGqs kmfObfsf] dfg lbG5 . pSt ljm| ofsnfkaf6
k|fKt lgisifc{ g;' f/ l3gL{ k|0ffnLdf l3gLs{ f] ;ª\Vof a9b\ } hfFbf oflGqs kmfObf klg a9b\ } hfG5 .
;/n oGqx¿sf] ko| f]uaf6 sfo{ ubf{ oflGqs kmfObf x'G5 / oflGqs kmfObfnfO{ lgDgfg;' f/
kl/eflift ul/G5 M

oflGqs kmfObf (MA) = nf8] (Load)/Okmf]{6 (Effort)

oflGqs kmfObfsf] PsfO xb'F }g lsgeg] of] b'O{ ansf] cgk' ft xf] .

pbfx/0fsf nflu l3gL{ ko| f]u u/]/ 200N sf] tfn} p7fpg 50N sf] an nufpg' k¥of] eg] o;af6
x'g] oflGqs kmfObf (Mechanical Advantage) MA = 200N / 50 N = 4 x'G5 .

o;sf] cy{ pSt l3gLs{ f] ko| fu] ubf{ 50N sf] ann] 4 u'0ff a9L tfn} p7fpg ;lsG5 .

sfoI{ fdtf (Efficiency)

lj|mofsnfk 8.2 df lx;fa ul/Psf] l3gLs{ f] ko| fu] af6 k|fKt x'g] sfo{ / l3gLd{ f ul/Psf] sfos{ f]
cgk' ftnfO{ k|ltztdf JoSt ubf{ pSt l3gL{ ko| f]u ePsf] pmhfd{ Wo] slt k|ltzt jf:tljs sfo{
ug{df vkt eof] eGg] hfgsf/L k|fKt xG' 5 . o;;uF } slt kl| tzt pmhf{ cGo ¿kdf ¿kfGtl/t

130 lj1fg tyf k|ljlwM sIff (

eof] eGg] hfgsf/L klg kf| Kt xG' 5 . pbfx/0fsf nflu olb pSt cgk' ftsf] dfg 75% cfPdf
xfdLn] l3gL{ tfGbf ko| fu] u/s] f] hDdf pmhfs{ f] 75 % ;bk' of]u x'G5 / afFsL 25 % pmhf{ 3if0{ fn]
ubf{ pTkGg xg' ] tfk, Wjlg, cflb zlStdf ¿kfGt/0f ePsf] a'lemG5 . t;y{ xfdLn] ko| f]u u/]sf]
l3gLs{ f] sfoI{ fdtf 75 % 5 . l3gL{sf] ko| fu] af6 k|fKt x'g] sfo{ pTkflbt sfo{ xf] . pTkflbt sfo{
eGgfn] oGqdf nf8] n] ug]{ sfon{ fO{ ae' mpF5 . ul0ftLo ¿kdf nV] bf,

pTkflbt sfo{ = nf8] n] ug]{ sfo{ = nf8] x nf]8 b'/L

To:t} l3gLd{ f ul/Psf] sfo{ nfut sfo{ xf] . nfut sfo{ eGgfn] oGqdf Okmf{]6n] u/]sf] sfo{nfO{
al' emG5 . ul0ftLo ¿kdf n]Vbf,

nfut sfo = Okmf]{6n] ug{] sfo{ = Okmf]{6 x Okmf6] { b/' L

;/n oGqdf pTkflbt sfo{ (Output work) / nfut sfo{ (Input work) sf] cg'kftnfO{
sfoI{ fdtf (Efficiency) elgG5 . o;nfO{ kl| tztdf JoSt ul/G5 . ul0ftLo ¿kdf

sfoI{ fdtf (Efficiency) = pTkflbt sfo{÷nfut sfo{ x 100 %

pTkflbt sfo{ / nfut sfo{sf ;"qnfO{ sfoI{ fdtfsf] ;q" df k|lji6 ubf,{

nf8]

Okmf]{6 x 100 %
sfoI{ fdtf -η_ = nf]8 b'/L

Okmf{6] b'/L

sfo{Ifdtf -η_ = oflGqs kmfObf x 100 %
ult cg'kft

;/n oGqx¿df pTkflbg sfo{ hlxn] klg nfut sfoe{ Gbf sd x'G5 . sfoI{ fdtf ztkl| tzt

xg' sf nflu ;Dk0" f{ nfut sfo{ pTkflbt sfod{ f kl/0ft ePsf] xg' k' 5{ . ;/n oGqx¿df x'g]

3if0{ fsf] sf/0fsf] ubf{ ;Dk"0f{ nfut sfo{ pTkflbt sfod{ f kl/0ft xg' ;St}g . h;n] ubf{ ;/n

oGqsf] sfo{Ifdtf hlxn] klg ztkl| tzteGbf sd x'G5 . ;/n oGqdf t]n jf lu|hsf] k|ofu] n]

3if0{ f 36fP/ o;sf] sfo{ Ifdtf sx] L a9fpg ;lsG5 .

k"0f{ oGq (Perfect machine)

nfut sfo{ / pTkflbt sfo{ a/fa/ ePsf] cj:yfdf sfo{Ifdtf ztkl| tzt xG' 5 . o:tf]
sfNklgs cj:yfsf] oGqnfO{ k0" f{ oGq (perfect machine) elgG5 . k"0f{ oGqdf oflGqs kmfObf
/ ult cg'kft klg a/fa/ x'G5 . o; lsl;dsf] oGqdf nfut sfo{df s'g} xf| ; cfpbF }g .
Jojxf/df 3if0{ f/lxt oGq ;Dej x'Fbg} . t;y{ k0" f{ oGq Jojxf/df ;Dej 5g} .

pbfx/0f

sg' } l3gL{ k0| ffnLsf] sfo{Ifdtf 80% 5 / oflGqs kmfObf 4 x'gsf nflu pSt k|0ffnLsf] l3gL{
;ªV\ of slt x'gk5{ < To; l3gL{ k|0ffnLdf 1000N sf] nf]8 p7fpg slt Okmf6{] rflxPnf <

lj1fg tyf k|ljlwM sIff ( 131

oxf,F
sfo{Ifdtf -M_ Ö 80%

oflGqs kmfObf (MA) = 4
nf8] (L) = 1000N
l3gL{ ;ªV\ of = ?
Okmf] {6 = ?
;q" cg;' f/,
sfoI{ fdtf Ö oflGqs kmfObf ÷ ult cg'kft x 100%
or, 80% = oflGqs kmfObf ÷ ult cgk' ft x 100%
or, ult cg'kft = oflGqs kmfObf ÷ 80 x 100
or, ult cgk' ft = 5
\ l3gL{ ;ª\Vof = 5

ca, Okmf{]6 = nf8] ÷oflGqs kmfObf or, Okmf6]{ = 1000/4

= 250N

2. 58s\ ] ;tx (Inclined plane)

lj|mofsnfk 8.3

km/s km/s ;txsf] nDafO ePsf j|mdzM Spring balance 60 cm
200 cm, 300 cm / 400 cm t;] f{] kmNofs weight
lng'xf];\ . tL kmNofsnfO{ 60 cm hlt
cUnf] 7fp“df 58s\ ] kf/L /fVg'xf;] \ . Pp6f lrq 8.5 58s\ ] ;tx
kmNofssf] ;tx;u“ 3if0{ f Psbd} Go"g xg' ]
lrKnf] ;tx ePsf] sf7sf] ;fgf] Ans
lng'xf];\ . pSt AnsnfO{ kfn}kfnf] sdfgL

t/fhs' f] k|of]u u/L tLgcf6] } 58s\ ] ;txx¿ dfly tfGbf nfUg] ansf] tYofª\s ;ª\sng
ug'x{ f];\ . k|fKt tYofª\snfO{ tnsf] tflnsf eg{'xf];\ / cfjZos kl/df0fx¿sf] lx;fa ugx'{ f];\ .

jm| =;= 58s] ;tx 58s] ;tx Uflt Nff]8 Okmf]6{ oflGqs sfoI{ fdtf
nDafO (l) prfO (h) cg'kft kmfObf

1. 200cm 60cm

2. 300cm 60cm

3. 400cm 60 cm

132 lj1fg tyf kl| jlwM sIff (

5nkmnsf nflu kZ| gx¿

1. 6s« af6 ;fdfg /fVbf -nf8] ubf_{ / emfbf{ -cgnf8] ubf_{ t;] f{] kmNofs lsg ko| fu] ul/G5 <

2. Psbd} 7f8f] vfnsf] -e'msfj sd ePsf]_ e¥ofª / e'msfj a9L ePsf] e¥ofªdWo] sg' df
plSng ;lhnf] xG' 5, lsg <

3. kxf8sf] 3d' fp/f] af6fsf] kmfObf s] xf] <

6«sdf ufxf| }F ;fdfgx¿ /fVg jf emfgs{ f nflu

58\s] agfP/ kmNofs k|of]u ul/G5 . 58\s] B
H
kmNofsaf6 ;fdfgnfO{ u'8fP/ ;lhn} /fVg tyf
C
emfg{ ;lsG5 . s'g} ufxf| F} ef/nfO{ cUnf] 7fpFdf
lrq 8.6 58s\ ] ;tx
;lhn} k'¥ofpg ko| f]u ul/g] le/fnf] ;tx ePsf]

pks/0fnfO{ 58s\ ] ;tx (Inclined plane) A

elgG5 .

;uF}sf] lrqdf 58s\ ] ;txdf 58s\ ] nDafO -AB=l_ n] Okmf6] {n] kf/ u/s] f] b/' L / 58s\ ]
;txsf] prfO -BC=h_ n] nf8] n] kf/ u/]sf] b'/L hgfp5F . t;y{ 58\s] ;txsf nflu

ult cgk' ft = Okmf6] { b'/L÷nf8] b'/L

= 58\s] ;txsf] nDafO÷58s\ ] ;txsf] prfO

VR = l / h 300 450 600

prfOnfO{ oyfjt /fvL 58\s] ;txsf]

nDafO a9fpFbf o;n] ;tx;Fu agfpg]

sf]0f 36b\ } hfG5 . 58s\ ] ;txsf]

nDafOnfO{ hlt nfdf] agfof] Tolt g} lrq 8.7 ;dfg prfO t/ km/s km/s le/fnf]
an b/' L a95\ . h;n] ubf{ ;/n oGqn] kfgf ePsf 58s\ ] ;tx
kj| w{g ug]{ an a9\5 / sfo{ ug{ ;lhnf]

x'G5 . 58s\ ] ;txdf o;sf] prfOnfO{ oyfjt /fvL

;txsf] nDafO a9fpFb} nfFbf ult cg'kft / oflGqs

kmfObf a9\5 . kxf8sf] le/fnf] hldgdf lgdf0{ f

xg' ] ;8sx¿df w/] } 3'DtLx¿ /fvL ;8ssf] nDafO

a9fOPsf] x'G5 . h;n] ubf{ psfnfdf uf8Lx¿sf]

OlGhg -engine_ af6 nfUg] ann] ef/L tfn} nfO{ ;lhn}

af]Sg ;lsG5 . lrq 8.8

lj1fg tyf k|ljlwM sIff ( 133

3. kfªu\ |f / la8 (Wheel and Axle)

ljm| ofsnfk 8.4
Pp6f kfªu\ f| / la“8sf] df8] n] lng'xf;] \ . o;sf] kl/lwdf df]6f] wfuf] ag] x{' f;] \ . laF8df
tf}nnfO{ emG' 8o\ fP/ kfª\u|fdf ePsf] 8f/] Laf6 Okmf{6] nufpg'xf;] \ . nufOPsf] Okmf]6{ gfKg
sdfgL t/fh' ko| fu] ug'x{ f;] \ . km/s km/s nf8] lngx' f];\ / cfjZos tYofªs\ ;ª\sng u/]/
tnsf] h:t} tflnsfdf e/L lx;fa ug{x' f;] \ M

k|ofu] nf8] Okmf6]{ oflGqs kmfObf kfª\uf| sf] la8“ sf] R/r sfoI{ fdtf
;ªV\ of cwJ{ of; (R) cwJ{ of; (r)
1.
2.
3.
4.

rªu\ f p8fpg n6\6fO ko| fu] x'G5 . To:t} u/L 9fs] fdf

x\ofG8n / ;fOsndf kfpbfg -paddle_ ko| f]u ul/Psf]

xG' 5 . oL pks/0fx¿ kfªu\ f| / la8F sf pbfx/0fx¿

xg' \ . logLx¿n] sfdnfO{ ;lhnf] agfpF5g\ . nfdf]

cw{Jof; ePsf] an] gf -kfªu\ f| _ / 5f6] f] cw{Jof; ePsf]

an] gf -la8F _ Pscfk;df hf8] ]/ Pp6} cIfdf ;uF } 3D' g lrq 8.9 kfªu\ f| / la“8

;Sg] u/L agfOPsf] ;/n oGqnfO{ kfª\uf| / la8F elgG5 . kfª\uf| df an nufO{ laF8df

emG' 8o\ fOPsf] tf}nnfO{ prfNbf o;df nufOPsf] an k|jw{g (magnify) x'G5 .

kfªu\ f| / laF8sf] k|ofu] u/L sfd ubf{ kfªu\ |f / la8F n] cfˆgf] cIfdf Ps kmGsf] nufpbF f
cfcfˆgf] kl/lw a/fa/ 8f]/Lsf] nDafO al] /g] jf km'Sg] x'G5 . kfª\u|f / laF8df Okmf]6{n]
kfª\u|fsf] kl/lw a/fa/sf] b/' L kf/ ubf{ nf8] n] laF8sf] kl/lw a/fa/sf] b'/L kf/ u5{ . t;y{
kfª\uf| / laF8df,

ult cgk' ft Ö Okmf6] { b/' L÷nf8] b'/L

Ö kfªu\ |fsf] kl/lw÷laF8sf] kl/lw

olb kfªu\ f| sf] cw{Jof; R / laF8sf] cwJ{ of; r eP,

ult cgk' ft Ö 2πR / 2πr

= R/r

t;y{ kfª\u|f / laF8df kfª\uf| sf] cwJ{ of; / la8F sf] cwJ{ of;sf] cg'kftn] o;sf] ult
cgk' ftsf] dfg lbG5 .

134 lj1fg tyf k|ljlwM sIff (

kfªu\ |f / laF8nfO{ lg/Gt/ufdL pQf]ns klg elgG5 lsgeg]

o;df pQf]nsdf h:t} nf8] / Okmf6{] cIfsf] bO' {lt/

x'G5 . o;sf] cIfdf kg{] sG] b|nfO{ kmnjm| d -F_ sf ¿kdf lng

;lsG5 . o;n] sfo{ ubf{ 360º 3'd]/ lg/Gt/ sfo{ ub5{ . o;

jm| ddf lrqdf bv] fOP h:t} kfªu\ |faf6 an nufpg a]l/Psf] lrq 8.10 lg/Gt/ufdL pQf]ns
8f]/Ln] 5f]Psf] Okmf6] { laGb' -A_ ;F+u;+uF } la8F df nf8] e'mG8\

ofpg a]l/Psf] 8f/] Ln] 5f]Psf] nf]8 laGb' -B_ klg kl/jt{g eO/xs] f] x'G5 .

;fwf/0f oGqaf6 sfo{ ubf{ tf}nnfO{ 5f]6f] ;dodf cyft{ l56f]

prfNg ;lsG5 . plt g} ;dodf ann] kf/ ug{] b'/LeGbf

tf}nn] kf/ ug{] b/' L a9L ePdf oGqn] sfos{ f] ju] a9fp5F .

pbfx/0fsf nflu kfªu\ |f / la8F -n6\6fO_ sf] laF8af6 an

nufpbF f plt g} ;dodf ann] kf/ ug]{ b/' LeGbf tf}nn] kf/ lrq 8.11 n6\6fOdf wfuf] a]b{} u/]sf]

ug{] b'/L a9L xG' 5 . o; cj:yfdf sfos{ f] ju] a9\5

cyft{ \ n66\ fOdf wfuf] rfF8f] rfF8f] al] /G5 . o;sf] l7s

ljk/Lt plt g} ;dodf tfn} n] kf/ ug{] b/' LeGbf ann]

kf/ ug]{ b'/L a9L ePdf oGqn] nufOPsf] an k|jwg{

(magnify) u5{ . pbfx/0fsf nflu rfnsn] :6]l/ª lrq 8.12 6«sdf xg' ] :6]l/ª\ lAXn /

lx\jn -steering wheel_ df nufPsf] an kj| w{g eO{ sf/df x'g] :6]l/ª\ lJXn

lgs} u|xf| F} uf8Lsf] kfªu\ |fsf] lbzf kl/jtg{ x'G5 .

:6]l/ª lx\jnsf] Jof; a9\bf an b/' L klg a9g\ ] ePsfn] a9L dfqfdf annfO{ k|jw{g ug{

6s« x¿sf] :6l] /ª lxj\ n sf/x¿df x'g] :6l] /ª lx\jneGbf 7n' f] agfOPsf] x'G5 .

4. km] ;f] (Wedge)

b}lgs hLjgdf rSss' f] k|ofu] n] kmnkm" n sf6g\ ],

r'n];Ln] t/sf/L sf6\g], aGr/fn] bfp/f lrg]{ cflb

sfo{ u/]sf] cjnfs] g ug{ ;lsG5 . oL sfo{x¿df

k|ofu] ePsf pks/0fx¿ km] ;f]sf pbfx/0fx¿

x'g\ . logdf x'g] wf/ b'Oc{ f]6f 58\s] ;tx ldn/]

ags] f] xG' 5 . o;/L Psflt/ df]6f] / km/flsnf]

efu ePsf] / csfl]{ t/ b'j} 58\s] :ftx ;fF3'/f]

xbF' } wfl/nf] ag]sf] pks/0f k]m;f] xf] . of] 58s] lrq 8.13 km] ;f]
;txsf] l;4fGtdf ags] f] x'G5 . lrq 8.13 df

k]m;f] j:t'leq l5/]sf] cj:yfdf o;sf] rf}8fO a/fa/sf] efudf 3if0{ f pTkGg xg' ] ePsfn]

pSt rf8} fO nf]8 b'/L xG' 5 . To:t} j:t'leq k]m;f] ;b}{ ubf{ an nufPsf] :yfgaf6 u8s] f]

efu;Dd an ;g]{ b/' L an b/' L x'G5 . k]m;f] k"0f{ ¿kn] j:t'leq u8]sf] cj:yfdf, km];fs] f]

rf}8fO Ö tfn} b'/L / km];f]sf] nDafO Ö an b'/L xG' 5 .

lj1fg tyf k|ljlwM sIff ( 135

km] ;fs] f] ult cgk' ft (Velocity ratio of wedge)

km;] f] Psflt/ km/flsnf] / df6] f] x'G5 eg] csfl]{ t/ bO' {cf]6f 58\s] ;tx ldn]/ wfl/nf] ag]sf]
xG' 5 . wfl/nf] efun] rflxPsf] lbzfdf 3if{0f lj?4 -tfn} _ sfo{ ug{ ;lhnf] agfp5F .

km];f]n] k0" f{ sfo{ ubf{,

ann] kf/ u/s] f] b/' L Ö km;] f]sf] ulx/fO Ö H

tfn} n] kf/ u/]sf] b/' L Ö km;] f]sf] rf8} f efu -6fpsf]_ sf] df6] fO Ö L

ult cgk' ft (VR) Ö Okmf]6{ b/' L÷nf]8 b'/L

= H/L lrq 8.14 ===

oflGqs kmfObf (Mechanical advantage - MA)

lrq 8.14 df E n] xfdLn] km];f]sf] rf}8f efu -6fpsf_] df nufPsf] an hgfpF5 . pSt an
nDa ¿kdf sf7leq ;5{ . To:t} W n] nf]8 (load) cyf{t k]m;f] j:t' jf sf7leq ul8Fbf
To;sf] ;txdf pTkGg xg' ] 3if{0fnfO{ hgfpF5 .

km] ;fs] f] oflGqs kmfObf

MA = W/E

pbfx/0f

;u+ }sf] lrqdf k]m;fs] f] k|of]un] sf7 lrg{ 200 N sf] an nufOPsf] 5 . k]m;f] sf7leq l5bf{
o;sf] ;txdf 600 N a/fa/sf] 3if{0f pTkGg xG' 5 eg] oflGqs kmfObf, ult cgk' ft / sfo{
Ifdtf lx;fa ugx{' f];\ .

lbOPsf,]

k]m;f]df nufOPsf] an -E_ Ö 200 N

k]m;f]sf] ;txdf pTkGg x'g] 3if0{ f (W) = 600 N

km];f]sf] ulx/fO -H_ Ö 10 cm

km];f]sf] rf8} f efu -6fpsf_] sf] df6] fO (L) Ö 2.5 cm

km] ;fs] f oflGqs kmfObf

MA = W lrq 8.15 ===
E

= 600 N =3
200 N

136 lj1fg tyf k|ljlwM sIff (

ultcg'kft (VR) Ö Okmf6] { b/' L÷nf]8 b'/L

Ö H = 10 =4
L 2.5

sfoI{ fdtf Ö oflGqs kmfObf ÷ ult cgk' ft x 100%
= 3/4 × 100% = 75 %

lbOPsf] km] ;f]sf] oflGqs kmfObf 3, ult cg'kft 4 / sfo{Ifdtf 75 % xG' 5 .

5. k]r (Screw)

b}lgs hLjgdf kr] sfF6Ln] sf7sf] 6j' m| f hf8] g\ ], Hofs :j|m'sf] lrq 8.16 ===
k|ofu] n] ef/ p7fpg], g6af]N6n] wft'sf kftx¿ s:g] cflb
u/s] f] cjnf]sg ug{ ;lsG5 . lrq 8.16 df b]vfOP h:t}
:j|m'df bO' c{ f6] f 58s\ ] ;txx¿ hf]l8Psf] wfl/nf] wfuf] :kfO/n
-spiral_ ¿kdf a]l/Psf] xG' 5 . To;n} ] k]rnfO{ :kfO/n 58\s] ;tx
-Spiral inclined plane_ elgG5 . kr] Ps lsnf h:t} an] gfsf/
(Cylindrical) j:td' f 58s\ ] ;tx a]l/P/ ag]sf] ;/n oGq xf] .

lrq 8.16 df b]vfP h:t} b'O{cf6] f wfuf]larsf] efunfO{ lkr -pitch_
elgG5 . k]rnfO{ Ps kmGsf 3'dfpFbf Ps lkr a/fa/sf] b'/L j:t'leq
;5{ . t;y{ x]8 -head_ sf] cwJ{ of; R ePsf] :jm| ' -k]r_ nfO{ Ps
kmGsf] 3d' fpFbf,

an b'/L Ö kr] df an nufOPsf] j[Qfsf/ kysf] kl/lw Ö 2πR

tf}n b'/L Ö j:t' leq ;g{] lkr a/fa/sf] b'/L Ö P

ult cgk' ft Ö 2πR/P

k]rsf oflGqs kmfObf lkrdf e/ k5{ . lkrsf] ;ª\Vof jf bO' { ug' flarsf] b/' L hlt sd
eof] TolQ g} sfo{ ug{ ;lhnf] xG' 5 .

;/n oGqsf] ;+ofh] gsf ¿kdf hl6n oGq

ljm| ofsnfk 8.5

kfgL tfGg] kDk, df]6/ uf8Lsf] OlGhg, nu' f l;pg] dl] ;g / sf/vfgfdf k|of]u x'g] 7n' f 7n' f
d]l;gsf] lrq jf >Job[Zo ;fdu|L kb| zg{ ul/Psf] cjnf]sg ugx{' f;] ,\ / lgDglnlvt k|Zgdf
5nkmn u/L lgisifd{ f k'Ug'xf];\ .

-s_ uf8Lsf] OlGhgnfO{ lsg hl6n oGqsf ¿kdf lnOG5 <

-v_ s] ;a} hl6n oGqx¿ ;/n oGqaf6 ag]sf x'G5g <

lj1fg tyf k|ljlwM sIff ( 137

hl6n ks| l[ tsf sfo{x¿ ug{ ;fwf/0f oGqaf6 ;Dej xbF' g} , h:tM} snsf/vfgfdf h8fg
ePsf OlGhgn] hl6n ks| l[ tsf] sfo{x¿ ug'k{ g]{ x'G5 . 7'nf 6s« x¿n] uxf| F} ef/ cf;] fg{]
sfdx¿ ub{5 . To:t} u/L a'n8f]h/n] af6f] vGg] sfo{ ub5{ . o;/L hl6n sfo{ ug{sf
nflu ljleGg k|sf/sf ;/n oGqx¿sf] ;+ofh] gaf6 hl6n oGq aG5g\ . h:fsf dfWodn]
l56f], ;lhnf] tyf yf]/} an nufP/ sfo{ ug{ ;lsG5 . o;/L b'O{ jf b'O{eGbf a9L ;fwf/0f
oGqx¿ ldnL ags] f oGqnfO{ hl6n oGq elgG5 . pbfx/0fsf nflu Car jack km];f] / kr]
ldnL ags] f] xG' 5 .

lj|mofsnfk 8.5

pbxf/0fdf lbOP h:t} xfd|f] j/k/ ko| f]u ePsf hl6n oGq sg' sg' ;/n oGqx¿ ldnL
hl6n ags] f 5g\ < ;f]wvf]h u/L tnsf] h:t} tflnsf agfO{ l6kf6] ug{'xf;] \ M

jm| =;= hl6n oGq ;/n oGq
1. j|m]g pQfn] s / l3gL{

xfd|f] b}lgs hLjgdf sfon{ fO{ ;lhnf], l56f] / lskmfotL agfpg ljleGg lsl;dsf hl6n
oGqx¿ k|of]u u/]sf x'G5fF} . tL hl6n oGqx¿ ;fwf/0f oGqaf6 ags] f x'G5g\ .

cEof;

!= tn lbOPsf k|Zgsf] ;xL pQ/df l7s lrx\g -√_ nufpgx' f];\ M

-s_ Ps rSs] crn l3gL{af6 oflGqs kmfObf geP klg o;sf] ko| f]u lsg ul/G5 <

-c_ ansf] dfqf a9fpg -cf_ j:ts' f] ult a9fpg

-O_ sfo{ ;lhnf] agfpg -O{_ ansf] lbzf kl/jt{g ug{

-v_ Ps kfª\u]| rn l3gL{sf] ult cg'kft slt x'G5 <

-c_ Ps -cf_ b'O{ -O_ tLg -O{_ rf/

-u_ @ ld6/ cUnf] 6s« df ;fdfg r9fpg 6m nfdf] kmNofs k|ofu] u/L 58\s] ;txsf]
lgdf{0f ul/Psf] 5, eg] pSt 58s] ;txsf] ult cg'kft slt xfn] f <

-c_ Ps -cf_ b'O{ -O_ tLg -O_{ rf/

-3_ k0" fo{ Gqsf] sfoI{ fdtf slt x'G5 <

-c_ 100% -cf_ 90% -O_ 75% -O_{ 50%

138 lj1fg tyf kl| jlwM sIff (

-ª_ Ps kfª\u|] 7n] fuf8f s'g sg' ;/n oGq ldnL ag]sf] xG' 5 <

-c_ kfªu\ f| / la8F tyf pQfn] s -cf_ l3gL{ / km;] f]

-O_ 58\s] ;tx / k]r -O{_ pQfn] s / km];f]

@= km/s n]Vg'xf];\ M

-s_ l3gL{ / kfªu\ |f tyf laF8

-v_ 58s\ ] ;tx / km];f]

-u_ Jack Screw / aGr/f]

-3_ pTkflbt sfo{ / nfut sfo{

#= sf/0f lbgx' f;] \ M

-s_ kxf8df r9g\ 3'dfp/f] af6f] agfPsf] x'G5 .

-v_ jm| g] nfO{ hl6n oGq elgG5 .

-u_ s'g} klg oGqsf] sfo{Ifdtf ztkl| tzt xbF' }g .

-3_ oGqsf] oflGqs kmfObf ult cgk' fteGbf sd xG' 5 .

-ª_ kfªu\ |f / laF8nfO{ lg/Gt/ufdL pQf]ns elgG5 .

-r_ oflGqs kmfObfeGbf ult cg'kft hlxn] klg a9L x'G5 .

$= k|Zgsf] pQ/ n]Vgx' f];\ M

-s_ ;/n oGq eg]sf] s] xf] < o;sf kmfObf n]Vg'xf;] \ .

-v_ hl6n oGq eg]sf] s] xf] < pbfx/0f;lxt JofVof ug'{xf];\ .

-u_ 58\s] ;txnfO{ pbfx/0f;lxt k:| 6 kfgx'{ f];\ .

-3_ km;] f] egs] f] s] xf] < pbfx/0f;lxt o;sf] dxŒj n]Vgx' f];\ .

-ª_ kr] s]nfO{ elgG5 < b}lgs hLjgdf k]rsf] k|ofu] s] s] sfdsf nflu ul/G5 <

-r_ l3gL{sf k|sf/nfO{ lrq;lxt kl/ro lbgx' f];\ .

-5_ kr] / km];fs] f oflGqs kmfObf / ultcgk' ft s;/L lgsflnG5 < lrq;lxt JofVof
ug{x' f;] \ .

-h_ 58\s] ;txsf oflGqs kmfObf / ult cg'kft s;/L a9fpg ;lsG5 < pbfx/0f;lxt
nV] g'xf;] \ .

lj1fg tyf kl| jlwM sIff ( 139

-em_ ;/n oGqsf oflGqs kmfObf / ult cg'kft s;/L lgsflnG5 < pbfx/0f;lxt nV] gx' f;] \ .

-`_ s'g} oGqsf] sfo{Ifdtf 75% eGgfn] s] al' emG5 < bl} gs hLjgdf k"0f{ oGq c;Dej h:t}
x'G5 < sf/0f;lxt JofVof ug{x' f];\ .

-6_ kfª\uf| / la8F sf] ult cgk' ft s;/L kQf nufOG5, lrq;lxt k:| 6 kfgx'{ f];\ .

-7_ lgDglnlvt hl6n oGq s'g s'g ks| f/sf ;/n oGq ldnL ag]sf] xG' 5, nV] gx' f];\ M

-c_ n'uf l;pg] dl] ;g -cf_ l:6h d]l;g

-O_ ;fOsn -O{_ 7n] fuf8f

%= ul0ftLo lx;fax¿ ug{x' f];\ M

-s_ lrqdf bv] fOPsf] 58s\ ] ;txsf 300N 5m
nflu oflGqs kmfObf, ult cg'kft / 20 m
sfo{Ifdtf lx;fa ugx{' f;] \ . 90kg

-Ans: MA = 3 , VR = 4, η =75%_

-v_ lrqdf rf/ rSs] l3gL{ k0| ffnL b]vfOPsf] 5 .
olb o;sf] sfo{ Ifdtf 80% 5 eg] pSt l3gL{ k0| ffnLsf nflu tnsf
kZ| gx¿ xn ugx'{ f;] \ M

-c_ 1000 N tf}nnfO{ p7fpg slt an nufpgk' 5{ <

-cf_ oflGqs kmfObf slt xG' 5 <

-O_ tfn} nfO{ 6 m dfly p7fpFbf x'g] nfut sfo{ / pTkflbt
sfo{ lx;fa ugx'{ f];\ .

-Effort = 312.5 N , MA = 3.2, nfut sfo{ Ö 7500 J, pTkflbt sfo{ Ö 6000 J_

-u_ kfªu\ f| / la8F sf] cwJ{ of; j|mdzM 20 cm / 5 cm 5 . o;af6 500 N p7fpg 250 N
an nufpgk' 5{ eg] o;sf oflGqs kmfObf, ult cgk' ft / sfo{ Ifdtf kQf nufpgx' f;] \ .
-Ans: MA = 2 , VR = 4, η = 50 %_

-3_ ;+Fus} f] lrqdf km];fs] f] ko| f]un] sf7sf d9' f lrb}{ 6 cm
u/]sf] bv] fOPsf] 5 . pSt k]m;fs] f] rf}8fO 6 cm /
ulx/fO 12 cm 5 . km];f]df 300 N an nufpFbf km];f]
500 N a/fa/sf] cj/f]Wf -tfn} _ pTkGg x'G5 eg]
o;sf oflGqs kmfobf, ult cgk' ft / sfoI{ fdtf 12 cm
lx;fa ug{x' f;] \ .

-Ans: MA = 1.67, VR = 2, η=83.33 %_ sf7sf] d9' f

140 lj1fg tyf kl| jlwM sIff (

( tfk
(Heat)

tn lbOPsf lrq;“u ;DalGwt s]xL hfgsf/L÷;fjwfgL pNn]v ul/Psf 5g\ . hfgsf/L÷
;fjwfgL;u“ ;DalGwt tYox¿ 5nkmn ugx{' f;] \ M

lrq 9.1 b}lgs hLjgdf ckgfpg' kg]{ sx] L ;fjwfgLx¿

;fjwfgL M kfgLsf] afkmn] kfN] gaf6 hfl] ugk' 5{ . ;fjwfgLM pDnb} u/s] f] kfgL afSnf] sfr“ sf] lunf;df
vGofpg' xb'“ }g .

;fjwfgLM /l] km|h/6] /nfO{ pkoS' t :yfg -kT| oIf 3fd gkg,{]

xfjfsf] ;j+ fxg ;xh} xg' _] df /fVgk' 5{ . l8k lkm|h/df kfgLsf

aft] n /fVbf 6Dd xg' ] u/L kfgL eg÷{' /fVg' xb“' g} ;fjwfgL M l;lnG8/ ;w“} 7f8f] /fv/] ko| fu] ugk{' 5{ .

lj1fg tyf k|ljlwM sIff ( 141

lrq 9.1

tftf] j:td' f k/df0f'÷c0fs' f] ult;uF } ltgdf x'g] ult ydn{ zlSt ;Gtn' g gx'Fbf;Dd tfk tftf] j:ta' f6

zlSt lr;f] j:td' f x'g]eGbf a9L xG' 5 . lr;f] j:td' f ;5{ .

lrq 9.1 df kfgLsf] afkmdf xg' ] c0f'x¿sf] tLj| rfnnfO{ nfdf] af0f lrx\gn] kb| z{g ul/Psf]
5 . 7f;] , t/n, / Uof;F kbfy{x¿df k/df0f'÷c0fl' arsf] b/' L / ltgLx¿sf] rfnsf] ult km/s
km/s x'G5 . dfly lrqdf bv] fOPsf] UofF; l;lnG8/df el/g] UofF; OGwg t/n cj:yfdf xG' 5 .
UofF;sf c0f'x¿sf] rfnsf] ultn] pSt Uof;F /flvPsf] ef8F fsf rfk l;hg{ f x'G5 . lrqdf s]xL
;fjwfgLx¿ klg pNnv] ul/Psf 5g\ . o; PsfOsf] cWoogsf jm| ddf dflysf lrqdf bv] fOPsf
;fjwfgL;Fu ;DalGwt yk ljm| ofsnfkx¿ pNn]v ul/Psf] 5 .

ydn{ zlSt, tfk / tfkjm| d (Thermal energy, heat and temperature)

lj|mofsnfk 9.1

-s_ tLgcf6] f las/x¿ ;ª\sng ug'x{ f;] \ . ltgdf pDns] f] kfgL, wf/fsf] kfgL / /]lkm| h/6] /
-refrigerator_ af6 lgsflnPsf] lr;f] kfgL 56' \6f566\ } /fVg'xf;] \ . k|To]sdf ;dfg dfqfdf
vfB /ª -food colour_ jf cla/ /fVg'xf;] \ / /ª ldl;b“ } u/s] f] cjnfs] g ug{'xf;] \ . olb
/ªsf s0fx¿sf] rfnnfO{ kfgLsf c0f'x¿sf] rfn ;dfg dfGg] xf] eg] s'gdf c0fx' ¿sf] rfn
;ae} Gbf tLj| x'G5, 5nkmn ug{'xf];\ .

-v_ Ps xftsf cf}“nfnfO{ pDn/] s]xL lr;f] ePsf] tftf] kfgLdf / csf{] xftsf cf“}nfnfO{ lr;f]
kfgLdf 8'afpg'xf;] \ . Ps ldg]6kl5 bj' } xft x6fpg'xf];\ / cf“}nfx¿ wf/fsf] kfgL el/Psf]
las/df /fVg'xf;] \ . tkfOs“{ f] ko| fu] / 5nkmnaf6 k|fKt x'g] lg:sif{ tnsf] h:t} tflnsfdf
n]Vgx' f;] \ M

cjnfs] g tftf] kfgLsf nflu lr;f] kfgLsf nflu wf/fsf] kfgLsf nflu

c0f'x¿sf] rfnsf] clt tLj| =============== ==============

cj:yf

xftsf cfnF} f tftf] lsgls tfk ================= =================

8'afpFbfsf] cg'ej kfgLaf6 cfn}F fsf]

/ To;sf] sf/0f 5fnfdf k|jz] u5{ .

kbfyd{ f yk' |} k/df0f' jf c0f'x¿ /x]sf xG' 5g\ . oL ;w}F rfn cj:yfdf /xs] f x'G5g\ . dgtftf]

142 lj1fg tyf k|ljlw M sIff (

kfgLdf ePsf c0f'x¿sf] ult zlSt lr;f] kfgLdf ePsf lg/kI] f zG" o tfkjm| d
c0fx' ¿sf] ult zlSteGbf a9L xG' 5 . tftf] kfgLdf xg' ] -absolute zero tempera-
c0fx' ¿sf] ult dgtftf] kfgLsf] eGbf emg} a9L xG' 5 . ture_ M of] Ps ;}4flGts ¿kdf
c0f'x¿sf] ult zlStsf] ofu] yd{n zlSt xf] . dgtftf] dflgPsf] z"Go ydn{ zlStsf]
kfgL, wf/fsf] kfgL / lr;f] kfgLsf] lk08 ;dfg ePsf] cj:yf xf] . o;sf] tfkj|md 0 K
cj:yfdf tftf] kfgLdf x'g] ydn{ zlSt ;a}eGbf a9L xG' 5 cyft{ \ -273° C xG' 5 .
/ lr;f] kfgLdf x'g] ydn{ zlSt ;a}eGbf sd xG' 5 .

kfgL pdfNbf aflx/af6 lbOg] zlStn] o;df ePsf
c0f'x¿sf] ult zlSt a95\ . kbfy{sf k/df0f' jf c0fx' ¿sf] cf};t ult zlStn] pSt kbfys{ f]
tfkj|md lgwf{/0f u5{ . tfkj|md j:td' f ePsf c0fx' ¿df ePsf] cf;} t ult zlStsf] ;r" sfªs\
xf] . tfkj|mdsf] P;=cfO{= PsfO -SI unit_ s]lNeg -K_ xf] . o;nfO{ ydf{]ld6/sf] ko| fu] u/L dfkg
ul/G5 .

Pp6f 8f8'df plDn/x]sf] kfgLsf nflu dfkg xg' ]

100oC / aflN6gdf /flvPsf] dgtftf] kfgLsf

nflu dfkg xg' ] 38oC jm| dzM c0f'x¿sf] cf;} t
ult zlSt a9L / sd ePsf] hgfpg] ;r" sfªs\
x'g\ . 8f8'sf] kfgLdf ePsf c0f'sf] ;ªV\ of
aflN6gdf ePsf] dgtftf] kfgLsf c0fx' ¿eGbf
lgs} sd x'G5 . To;}n] c0fx' ¿sf] ultzlStsf]
cf;} t 8f8'sf] kfgLsf nflu a9L x'G5 . b'jd} Wo]
c0f'x¿sf] ult zlStsf] of]u eg] dgtftf]
kfgLdf a9L x'G5 lsgls o;df c0f'x¿sf]
;ª\Vof 8f8d' f ePsf c0fx' ¿sf] ;ªV\ ofeGbf lrq 9.2 yd{n zlSt a9L / tfkqmd sd xg' ] cj:yf
lgs} w/] } x'G5 . t;y{ 8f8d' f plDn/x]sf] kfgLsf]
eGbf aflN6gdf ePsf] dgtftf] kfgLdf ydn{ zlSt a9L xG' 5 . kbfys{ f] yd{n zlSt o;sf]
lk08 / c0fx' ¿sf] cf};t ult -tfkjm| d_ df lge{/ ub5{ . dfly pNn]v ePcg';f/ b'j}df ePsf]
kfgLnfO{ ld;fpFbf ydn{ zlSt eg] 8f8'df plDn/xs] f] kfgLaf6 aflN6gsf] dgtftf] kfgLdf
;5{ . o;/L tfkjm| dsf] leGgtfn] Ps 7fpaF f6 csf{] 7fpdF f k|;f/0f x'g] zlSt tfk xf] . cGo
zlStx¿sf] h:t} tfksf] P;= cfO={ PsfO klg hn' -J_ xf] . o;nfO{ Sofnfl] /ld6/ -Calorimetre_
sf] k|of]u u/L dfkg ul/G5 .

tfk s'g} j:td' f ;l~rt xF'bg} . of] Ps j:t'af6 csf{] j:td' f ;g]{ yd{n zlStsf] kl/df0f xf] .
tfk k|;f/0f xb'F f Pp6f j:t'sf] yd{n zlSt 365\ / csf{] j:ts' f] ydn{ zlSt a95\ . of] ;~rfng,
;j+ fxg / ljls/0fåf/f k;| f/0f xG' 5 . xfdLn] sg' } j:tn' fO{ ;dfTbf tfk z/L/df kj| z] u/d] f tftfs] f]
cge' j xG' 5 / tfk z/L/af6 aflxl/Pdf lr;fsf] cge' j xG' 5 . tfk a9L tfkjm| d ePsf j:ta' f6
sd tfkjm| d ePsf j:td' f ta;Dd k;| f/0f xG' 5 ha;Dd bj' d} f ;dfg tfkjm| d xbF' g} .

lj1fg tyf k|ljlwM sIff ( 143

tfkn] cfotgdf kg{] c;/ -Effect of heat on volume_

ljm| ofsnfk 9.2 lj|mofsnfkdf pNn]v ul/Pcg;' f/
lrq 9.3 kmnfdsf] 8Nnf] / l/ªsf] lrq
Pp6f kmnfdsf] e'mG8o\ fpg ldNg] 8Nnf] / ;fx] L
;fOhsf] 8Nnf] l7Ssn] l5g{] l/ª lngx' f];\ .
lrqdf bv] fOP h:t} kmnfdsf] 8NnfnfO{ sx] L
;do ttfpgx' f];\ / l/ªaf6 l5/fpg] sfl] ;;
ug'{xf];\ . sx] L ;dokl5 8Nnf] ;]nfpg lbg'xf];\
/ kg' M 8NnfnfO{ l5/fpg] ko| f; ug'{xf;] \ . yd{n
zlSt jf tfksf] kl/efiffsf cfwf/df tkfOs“{ f]
cjnfs] g / To;sf sf/0faf/] 5nkmn u/L
lgisif{ nV] gx' f;] \ .

cjnfs] g JofVof lgisif{

8Nnfdf ePsf 8Nnfdf ePsf 8Nnfdf ePsf
c0f'x¿sf] ult zlSt c0fx' ¿larsf] cfsif0{ f c0fx' ¿larsf] b'/L

kmnfdsf] 8Nnf] a95\ ============ ================== ============
ttfP/ l/ª\af6
l5/fpg vfH] bf
==================

============= ============= ============ ============ ============

tfk k|;f/0faf6 j:t'df yd{n zlSt ylkbF f o;sf c0f'x¿sf] cf}ift ult zlSt a9\5 cyf{t\
tfkj|md j[l4 xG' 5 . c0f'x¿ Ps csf{;+Fu hf8] n] 7f]lsG5g\ . j:t'sf c0f'x¿larsf] b'/L a9\5 /
;dud| f j:t'sf] cfotg a9\5 . o;sf] l7s ljk/Lt j:t'sf] ydn{ zlSt aflx/ hfbF f c0f'x¿sf]
cf;} t ult zlSt 36b\ f tfkj|md 36\5 / j:t' vl' DrG5 . o;/L clwsf+z kbfyx{ ¿sf] tfkj|md
j[l4 xFb' f cfotg a95\ / tfkj|md 36\bf v'lDrG5g\ .

kfgLsf] c;fwf/0f k;| f/ (Anomalous expansion of water)

clwsfz+ kbfyx{ ¿nfO{ ttfpbF f ltgLx¿sf] cfotg a9\5 . kfgLnfO{ ttfpFbf o;sf] cfotg
a9g\ ] eP tfklg 0°C bl] v 4°C ;Dd o;sf] cfotg a9\gs' f] ;6\6f 36\5 . kfgLnfO{ lr:ofpFbf
klg 4oC ;Dd cfotg 365\ eg] 4°C af6 0°C ;Dd o;sf] cfotg a9\5 . kfgLsf] of] cgf}7f]
u'0fnfO{ cgf}7f] k;| f/-Anomalous expansion_ elgG5 .

sg' } klg kbfys{ f] 3gTj To;sf] cfotg;+uF JoT' j|mdfgk' flts xG' 5 .

144 lj1fg tyf kl| jlw M sIff (

cyf{t kbfy{sf] lk08 l:y/ /xL cfotg a9]df pSt
j:ts' f] 3gTj 36\5 / olb cfotg 36]df pSt j:ts' f]
3gTj a9\5 . To;n} ] 4°C df kfgLsf] cfotg Go"gtd
/ 3gTj clwstd x'G5 . lrq 9.4 sf] uf| kmn] kfgLsf]
cfotg / 3gTjlarsf] ;DaGw bv] fp5F g\ . 4oC af6
kfgL ttfpg jf lr;f] kfbf{ o;sf] cfotg a95\ / 3gTj
365\ .

lrq 9.4 kfgLsf] cfotg / 3gŒj larsf] ;DaGw

kfgLsf] c;fwf/0f k|;f/sf c;/x¿ (Effects of anomalous expansion of water)

w/] } lr;f] xg' ] :yfgx¿df hf8f] ofddf

jftfj/0fsf] tfkjm| d 0°C eGbf tn

em5{ . tfn, kfv] /L cflbdf ;txsf] kfgLsf]

tfkj|md 4°C lt/ emb{} hfFbf a9L 3gTj

ePsf] kfgLsf] tx tnlt/ a:5 / tnsf]

txsf] kfgL dfly wsl] nG5 . kfgLsf] tfkjm| d

4°C xg' ] lalQs} of] ;ae} Gbf a9L 3gTjsf]

xG' 5 / lkFwdf hfG5 . ha j/k/sf] tfkj|md

j|mdzM 4°C af6 0°C ;Dd em5{, kfgLsf] lrq 9.5 tfnsf] ;txdf hd]sf] a/kmdl' g
;txsf] tfkjm| d klg ;fx] Lcg;' f/ 365\ . hLljt hnLo hLj
kfgLsf] tfkjm| d 36\g] jm| dcg';f/ o;sf]

cfotg a9\5 / 3gTj klg tbg;' f/ sd

x'G5 . sd 3gTj ePsf txx¿ jm| dzM ;ae} Gbf tn /x]sf] 4°C sf] kfgLsf] txeGbf dfly

xG' 5g\ . ;txsf] kfgL 0°C df kl/0ft xFb' f, a/km aG5 / tnlt/ /xs] f] kfgLsf] ;txdf t}/G5 .

a/km tfksf] sr' fns ePsfn] o;d'lgsf] kfgLsf] tfkj|md 0°C eGbf dfly /xG5 . To;n} ] df5f

/ cGo hnLo kf| 0fLx¿ a/kmsf] tx tn kfgLdf hLljt /xg ;S5g\ .

lxpFb ofddf jf w]/} lr;f] :yfgdf jftfj/0fsf] tfkjm| d
4°C af6 jm| dzM 36b\ } hfFbf kfOkleqsf] kfgLsf] cfotg
a9b\ } hfG5 / o;n] kfOknfO{ bafa lbG5 . kfgL hd]/ a/km
aGbf rfk cTolws eO{ kfOk km6' \g ;S5 . o:t} lsl;dsf]
bafa k0" f{ ¿kn] kfgL el/Psf] aft] nnfO{ /l] k|mh/6] /sf] l8k lrq 9.6 kfgLsf kfOkleq hds] f] a/km
lk|mhdf /fVbf klg xG' 5 . h;n] ubf{ kfgLsf] aft] n rls{G5 .

lj1fg tyf kl| jlwM sIff ( 145

klUng] / plDng] ljm| of (Melting and boiling)
lj|mofsnfk 9.3
tn lbOPsf lrqx¿af6 kbfy{sf] kUng] / pDng] ljm| ofdf ltgsf c0fx' ¿sf] el" dsf cjnfs] g
ugx'{ f];\ . o;sf ;fy} kUng] lj|mof / pDng] lj|mofdf tfksf] e"ldsfaf/] 5nkmn ugx'{ f;] \ .

lrq 9.7 7f;] af6 t/n / t/naf6 Uof;“ df kl/jtg{ xb“' f k/df0f÷' c0fs' f] cj:yfdf xg' ] kl/jtg{

kbfy{ klUnbF f 7f;] cj:yfaf6 t/n cj:yfdf kl/jt{g x'G5 . sg' } 7f;] kbfy{nfO{ ttfpbF f o;df
ePsf k/df0f'÷c0fx' ¿n] zlSt kf| Kt ub{5g\ . tfk lg/Gt/ lbbF f k/df0f'÷c0fx' ¿ bt'| ¿kdf
sDkg x'G5g\ . ltgLx¿larsf] cfsif0{ f an sdhf/] x'G5 / Pscsf{af6 6f9f hfG5g\ . h;n]
ubf{ 7f;] t/n aG5 . pSt t/ndf lg/Gt/ tfk lbOPdf kg' M To;sf] cj:yfdf kl/jt{g cfO{
Uof;F aGg ;S5 . pDng] lj|mofn] kbfy{ t/n cj:yfaf6 Uof;F df kl/jtg{ x'G5 . t/nnfO{ lg/Gt/
ttfpFbf o;sf c0fx' ¿n] clgoldt rfn k|bz{g ug{ ;?' u5{g\ . of] rfnn] c0f'x¿nfO{ yk 6f9f
agfpF5 . t/nsf c0fx' ¿sf] ult zlStn] kb} f ug]{ an ltgLx¿larsf] cfsif0{ f -Inter-molecular
force_ eGbf a9L xF'bf t/n kbfy{ Uof;F jf afkmdf kl/jtg{ x'G5 .
ljm| ofsnfk 9.4
tkfO“{ cjl:yt :yfgdf xg' ] jfod' 08nLo rfk tyf a/kmsf] kUng] tfkjm| d / kfgLsf] pDng]
tfkj|mdsf] dfkg ugx'{ f];\ . log} tfkj|mdsf] g]kfnsf t/fO{, kxf8 tyf lxdfnL e]usf ljleGg
:yfgx¿df dfkg ul/Psf tYofª\sx¿ ;ªs\ ng ug'x{ f];\ . tYofªs\ sf] tn' gfTds ljZn]if0fsf
cfwf/df lgisif{ n]Vg'xf;] \ .
:6]G88{ dfg M a/kmsf] kUng] tfkjm| d Ö =========, kfgLsf] pDng] tfkjm| d Ö =========
;ª\sng ul/Psf] tYofªs\ M
:yfg jfo'd08nLo rfk a/kmsf] kUng] tfkjm| d kfgLsf] pDng] tfkj|mdsf lgisif{

146 lj1fg tyf k|ljlw M sIff (

sg' } lglZrt 7fpdF f kUng] / pDng] lj|mof k|dfl0fs rfk -standard pressure_ 1
lglZrt tfkj|mddf dfq x'G5 . kbfy{ 7f;] P6\dfl] :kol/s -1 atmospheric- 1 atm_
cj:yfaf6 t/n cj:yfdf kl/jtg{ xg' xG' 5 . of] ;db' |L ;txdf xg' ] jfo'd08nLo
cfjZos tfkj|md pSt 7f;] kbfys{ f] kUng] rfk xf] .
laGb' -melting point_ xf] / t/n cj:yfaf6 1 atm = 760 mmHg = 101325 Pa xG' 5 .
UofF; cj:yfdf kl/jtg{ x'g cfjZos tfkj|md
pSt kbfys{ f] pDng] laGb' -boiling point_ xf] .

tflnsf M kd| fl0fs rfk -standard pressure_ df kUng] laGb' / pDng] laGb'

kbfy{ kUng] tfkj|md pDng] tfkj|md kbfy { kUng] tfkjm| d pDng] tfkj|md

kfgL 0°C 100°C kf/f] -39°C 357°C
cNsf]xn -115°C 78°C kmnfd 1538°C 2862°C

plDng] laGb'df rfksf] c;/ (Effect of pressure on boiling point)

lj|mofsnfk 9.5

Pp6f l;l/Gh / las/df pDn]sf] kfgL lngx' f];\ . las/df ePsf] plDng 5f8] ]sf] tftf]
kfgLnfO{ l;l/Ghdf Ps rf}yfO hlt x'g] u/L egx{' f;] \ . ca l;l/Ghsf] gh' nnfO{ cfn“} fn]
lyRgx' f];\ / lk:6gnfO{ tfGgx' f;] \ .

las/sf] kfgLsf] cjnfs] g JofVof
tfkj|md ====================
lk:6g tfGgk' j" { lk:6g tflg;s] kl5sf]
kfgLsf] cj:yf kfgLsf] cj:yf

kfgLsf] ;txdflysf] bafa Ps P6d\ f]l:kmo/ jf:kLs/0f ljm| of / pDng] lj|mof km/s
-1 atm_ x'Fbf 100°C tfkjm| ddf dfq kfgL xg' \ . t/nsf] jfikLs/0f ljm| of ;a}
pDnG5 . o; cj:yfdf kfgLleqsf] jfikn] tfkj|mddf eO/x]sf] x'G5 . of] sj] n
ubf{ pTkGg rfk / o;sf] ;txdf kg{] rfk t/nsf] ;txaf6 clws ult zlSt ePsf
a/fa/ xG' 5 . kfgL pDnbf o;sf] ;txleqsf] c0f'x¿ p8]/ hfg] k|ljm| of xf] . pbfx/0fsf
jfiksf kmf]sfx¿ ;txdf cfP/ k'm65\ g\ / jf:k nflu jf:kLs/0fsf sf/0fn] lehs] f] nu' f
;txaf6 p8/] hfG5 . kfgLsf] ;tx dflysf] ;fwf/0f tfkj|mddf g} ;'S5 .
rfk Ps P6\df]l:kmo/ -1 atm_ eGbf a9L ePdf
kfgLsf c0fx' ¿nfO{ ;txaf6 p8/] hfg ;fdfGo
cj:yfdf eGbf a9L zlSt cfjZos k5{ . h;n]

ubf{ kfgLsf] pDng] laGb' 100oC eGbf a9L
xG' 5 .

lj1fg tyf kl| jlwM sIff ( 147