& an / rfn
(Force and Motion)
af6n' Lsf] a; ofqf
;Fu+ s} f] lrqdf bv] fOPsf] af6f] xFb' }
af6'nL :yfg A df a; r9/] :yfg
B df kl' ug\ . pgn] a; r9s] f] :yfg
A df s]xL ;do a; l:y/ cj:yfd}
lyof] . a; rfnsn] OlGhg -engine_
:6f6{ u/k] l5 OlGhgn] nufPsf] ann]
ubf{ a; la:tf/} u'8g\ ;'? u¥of] . sx] L
;dokl5 a; hf8] n] xO' Flsof] . af6fdf
a; sxLF la:tf/} u8' g\ ] / sxLF hf8] n]
x'OlF sg] eO/x]sf] lyof] . 7fpF 7fpFdf
a;df as|] nufpbF f pgsf] z/L/
cufl8 lt/ x'lQg] uYof{] . lrq 7.1 =b'O{ :yfg A / B hf]8g\ ] af6fsf] u'un gS;f
af6fdf a; ljleGg lbzflt/ u8' g\ ] uYof]{ . af6'nLn] 3D' tLx¿df rfnsn] :6]l/ª xl\ jn -steering
wheel) 3'dfP/ a;sf] lbzf kl/jtg{ u/]sf] cjnf]sg ul//xs] L lyOg\ . s] tkfOFnfO{ hfgsf/L
5 t, a;sf] :6]l/ª xl\ jn laub| f s] x'G5 <
af6n' Ln] a; u8' b\ } ubf{ af6f] 5p] sf af6f] b'/L nv] ]sf :tDex¿ x]b}{
;docg;' f/ kf/ u/]sf] b/' L klg l6Kb} uOg\ .
;do -minutes df_ 10 25 30 40 50 …. lrq 7.2 =3D' tLdf a;
kf/ u/]sf] b'/L -km df_ 5 10 a; /fl] sPsf] 15 20 …..
af6n' Ln] l;wf af6fdf a; Psgf;n] ul' 8/x]sf] cj:yfdf rfnssf]
cufl8 /xs] f] l:k8f]ld6/ -speedometer_ df 50 km/h kb| z{g ePsf]
bl] vg\ . pgn] an] f a]nfdf o:t} gfk x]//] a; ;dfg cj:yfn] ul' 8/x]df
l;wf af6fsf] cufl8sf] b'/L kf/ ug{ nfUg] ;dosf] lx;fa ub{} uOg\ .
af6'nLn] cfk\mgf] uGtJodf k'uk] l5 rfns;+Fu ;fw] ]/ a;n] ofqfel/ lrq 7.3= a; rfnssf]
kf/ u/]sf] b/' L 74 km /xs] f] kQf nufOg\ . pSt kf/ u/s] f] b/' L / b/' L cufl8 ePsf] l:k8f]ld6/
kf/ ug{ nfu]sf] ;dosf cfwf/df cf;} t ju] kQf nufOg\ . pgn] 3/
ku' k] l5 OG6/g]6sf] ko| fu] u/L uu' n d]k vf]hL u//] cfkm" n] to u/s] f]
lj1fg tyf kl| jlwM sIff ( 97
ofqfdf :yfg A af6 :yfg B df k'Ubf 25.5 km blIf0f kj" { :yfgfGt/0f -displacement_ ePsf]
kQf nufOg\ .
kZ| g -s_ OG6/g6] sf] k|of]u u/L lrq 7.1 df bv] fOPsf] gS;f s;/L xg] { ;lsG5 < sIffdf
5nkmn ugx{' f];\ .
kZ| g -v_ pknAw k|ljlwsf] k|ofu] 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 x'g] :yfgfGt/0f kQf nufpgx' f;] \ .
a]u / ult (Speed and velocity)
lj|mofsnfk 7.1
lrq 7.4 n] af6n' Lsf] ofqfsf jm| ddf af6fdf a; ljleGg lbzflt/ dfl] 8Psf] bv] fp“5 .
tkfO“{n] klg ljBfnosf] rp/df 50 m nfdf] lkmtf (measuring tape_ jf 8f]/Lsf] ;xfotfn]
o:t} lsl;dsf] 6«ofs lgwf{/0f ugx{' f;] \ . Pp6f :6k jfrsf] ko| f]u u/L s'g} ;fyLnfO{
af6fdf sxL“ lx8“ \b} / sxL“ la:tf/} bub' }{ Ps 5]paf6 csf]{ 5p] df kU' g nfu]sf] ;do lx;fa
ug{'xf];\ . af6fsf] ljleGg v08df ;fyLsf] rfn s'g sg' lbzflt/ lyof] < :yfgfGt/0f,
cf};t j]u tyf sg' } lglZrt v08df cf;} t ult lx;fa ugx{' f;] \ .
c f};t j]u ( Vav)= kf/ u/s] f] b'/L (d) = ... m/s
nfus] f] ;do (t)
j:t'n] lglZrt lbzflt/ k|lt ;s] ]G8df kf/ u/]sf] cf};t b'/L,
cf};t ult (AV) = lglZrt lbzfdf kf/ u/s] f] b/' L (s) = m/s …lbzf
pSt b'/L kf/ ug{ nfus] f] ;do (t)
lrq 7.4 df a;n] :yfg A af6 :yfg F ;Dd kf/ u/s] f] hDdf b'/L ABCDEF ld6/ xG' 5 /
:yfgfGt/0f AF ld6/ pQ/ kj" { x'G5 . s'g} rfn cj:yfdf /x]sf j:t'n] kf/ u/s] f] hDdf nDafO
b'/L -distance_ xf] . b'/LnfO{ s'g} lglZrt lbzf pNnv] gu/L dfgn] dfq JoSt ul/g] ePsfn] of]
Ps :s]n/ kl/df0f xf] . kf| /lDes :yfgaf6 lglZrt lbzfdf uP/ clGtd :yfgdf kU' bf j:tn' ]
kf/ u/s] f] ;a}eGbf 5f]6f] b'/L :yfgfGt/0f
-displacement_ xf] . jf:tjdf of] b'O{ laGbl' arsf]
l;wf /v] Lo b/' L xf] . :yfgfGt/0fnfO{ JoSt ubf{
dfg;uF+ } lbzf klg pNnv] ul/g] ePsfn] of] Ps
e]S6/ kl/df0f xf] .
b'/L ABCDEF nfO{ pSt b'/L kf/ ug{ nfus] f] lrq 7.4 a;n] kf/ u/s] f] b'/L / o;sf] :yfgfGt/0f
;don] efu ubf{ a]usf] dfg k|fKt xG' 5 .
a;n] af6fsf ljleGg v08x¿df sg' } lglZrt
lbzflt/ kf/ u/]sf] b'/LnfO{ pSt b'/L kf/ ug{
98 lj1fg tyf k|ljlwM sIff (
nfu]sf] ;don] efu ubf{ ;f] v08df a;sf] ult cfpF5 . lrq 7.4 sf] :yfg B df a; k|lt;sG] 8
10 ld6/ b'/L kf/ ub}{ kj" {lt/ uO/xs] f] lyof] . :yfg C df a;sf] ult kl/jt{g eP/ kl| t ;s] G] 8
20 ld6/ blIf0f k"j{ lbzflt/ ePsf] 5 . af6fsf] DF v08df a;sf] ult 15 ld6/ pQ/kj" { /xs] f]
5 . t;y{ j:tn' ] kl| t PsfO ;dodf kf/ ug{] b/' L pSt j:ts' f] j]u -speed_ xf] / j:t'n] lglZrt
lbzflt/ k|lt PsfO ;dodf kf/ u/]sf] b'/L pSt j:t'sf] ult -velocity_ xf] . olb sg' } lglZrt
lbzflt/ ul' 8/x]sf] j:t' slxn] l56f] / slxn] l9nf] u/L u8' b\ } 5 eg] To:tf] rfn c;dfg rfn
xG' 5 . c;dfg ultn] lglZrt lbzfdf u'l8/x]sf] j:t'n] nIodf k'Ubf To;n] kf/ u/]sf] hDdf
b'/LnfO{ pSt b'/L kf/ ug{ nfu]sf] ;don] efu ubf{ kf| Kt x'g] ult Tof] j:ts' f] cf;} t ult xG' 5 .
ju] nfO{ :s]n/ kl/df0f / ultnfO{ e]S6/ kl/df0f xg' \ . ultsf] dfgdf kl/jtg{ geP/ s]jn
lbzf kl/jtg{ xFb' f ult
kl/jt{g xG' 5 t/ j]u l:y/
/xG5 . lrq 7.5 df bv] fOP
h:t} ;Gbe{ laGb' -reference
point_ sf cfwf/df sg' }
Ps lbzfdf uO/x]sf]
j:tn' ] l7s ljk/Lt lbzfdf
hfbF f ult wgfTdsaf6 lrq 7.5 ;Gbe{ laGbc' g;' f/ wgfTds ult / C0ffTds ult
C0ffTds xG' 5 . j:ts' f] ju]
;wF} wgfTds x'G5 .
kj| ]u -Acceleration_
ljm| ofsnfk 7.2
p2]Zo M j:td' f x'g] ult kl/jtg{ sf] cjnf]sg ug'{
cfjZos ;fduL| M Pp6f ;dtn ;tx ePsf] sl/a 3 m nfdf] sf7sf] kmn]s, s]xL
lstfax¿, uR' rf jf ;fgf] es'G8f,] :6k jfr, rs jf k]lG;n
ljlw M
1. sf7sf kmns] nfO{ lstfax¿sf] cf8 nufO{ /fVgx' f;] \ .
2. kmn]ssf] dflyNnf] 5p] af6 uR' rf jf esG' 8f] u'8fpgx' f];\ .
3. es'G8f] ul8/xbF f Ps hgfn] :6k jfrsf] ;xfotfn] k|Tos] 1 ;s] G] 8sf] hgfp ug{'xf;] \
/ csf{] ;fyLn] kmns] df u'8b\ } u/s] f] j:t' k'us] f] :yfgdf lrxg\ nufpgx' f];\ .
4. u'Rrf jf esG' 8f]sf] rfn cjnf]sg ug{'xf;] \ .
5nkmn / lgisif{ M u'Rrf jf esG' 8fs] f] ult s:tf] /x\of,] 5nkmn ug'{xf;] \ .
lj1fg tyf kl| jlwM sIff ( 99
rfn cj:yfdf /x]sf j:tx' ¿df ;dfg ult gxg' ;S5 .
ul' 8/xs] f a;sf] ult sxLF a9b\ } a9b\ } hfg] / sxLF 36b\ }
36\b} hfg] x'G5 . Psgf;sf] le/fnf] ;txdf kY[ jLsf] u?' Tj
ann] u'8b\ } u/s] f] j:t'df kl| t;]sG] 8 ult a9\b} hfG5 . kl| t
PsfO ;dodf x'g] ult kl/jtg{ nfO{ kj| ]u elgG5 . o;sf]
SI PsfO m/s2 xf] .
clGtd ult (v) – ;?' sf] ult (u)
k j| u] ( a) = ;do (t)
k[YjLsf] u'?Tjansf] sf/0f :jtGq ¿kdf vl;/x]sf] j:t'df
pTkGg x'g] k|j]u u'?Tj k|j]u xf] . o;nfO{ 'g' n] ;ª\st]
ul/G5 . kY[ jLsf] ;txdf o;sf] cf};t dfg 9.8 m/s2 xG' 5 .
u8' \b} u/s] f] a;df lj:tf/} a|s] nufpbF f o;sf] ult 36\b}
u/s] f] cg'ej ug{ ;lsG5 . sg' } rfn cj:yfdf /xs] f] j:t'sf] lrq 7.6 =:jtGq ¿kn] vl;/xs] f] j:t'sf]
kl| tPsfO ;dodf ult 36\g] b/nfO{ ultxf| ; -retardation_
elgG5 . o;nfO{ C0ffTds k|j]u klg elgG5 . 3s ;Ddsf] rfn
5nkmnsf] kZ| g
lrq 7.6 df :jtGq v;fOsf] cjnf]sgaf6 k|fKt x'g] tYofªs\ lbOPsf] 5 . pSt tYofªs\ nfO{
cfwf/ dfgL tn ul/Psf lx;faaf6 s] lgisif{ lgsfNg ;lsG5 <
cf;} t ult (vav) = cf;} t ult (vav) =
lglZrt lbzfdf kf/ u/]sf] 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] sG] b|lt/ = 14.7 m/s k[YjLsf] sG] bl| t/
:jtGq ¿kn] vl;/xs] f] j:t'sf] rfnsf] lbzf lglZrt eP tfklg kl| t;]sG] 8 kf/ ug]{ b/' L km/s km/s
x'G5 . To;n} ] of] c;dfg ult xf] . t/ :jtGq v;fOsf] cj:yfdf j:t'sf] k|ju] eg] kl| t;s] ]G8 ;dfg
x'G5 . j:t' ;dfg k|j]un] l;wf /v] fdf v:bf jf u8' \bf j:ts' f] k|f/lDes ult / clGtd ultsf]
dWosn] pSt j:ts' f] cf;} t ult lbG5 . t;y{ l;wf /v] Lo rfndf ;dfg k|ju] n] ePsf] j:ts' f
nflu
c f};t u lt (Vav) = ;'?sf] ult -u_2± clGtd ult -v_
100 lj1fg tyf k|ljlwM sIff (
l;wf /v] Lo rfnsf ;dLs/0fx¿ -Equations of linear motion_
l;wf /v] Lo rfnsf ;dLs/0fdf j:t'sf] ;'?sf] ultnfO{ u, clGtd ultnfO{ V kf/ u/s] f] b/' LnfO{
s pTkGg xg' ] kj| u] nfO{ a, j:t' rfn cj:yfdf /xFbfsf] ;donfO{ t n] hgfOG5 .
1. l;wf /v] Lo rfnsf nflu ;?' sf] ult -u_, clGtd ult -v_, k|j]u -a_ / ;do -t_ ;DaGwL
;dLs/0f
dfgf,}F s'g} l;wf /v] Lo rfndf /x]sf] j:ts' f] ;?' sf] ult -u_ Psgf;n] kl/jtg{ xb'F }
s]xL ;do -t_ kl5 clGtd ult -v_ df kl/0ft eof] .
clGtd ult – ;?' sf] ult
k|j ]usf] k l/efiffc g';f/, k|j]u = ;do
a= v-u
t
at = v - u
v = u+at ………………….. (i)
pbfx/0f 7.1
lqej' g cGt/fl{ i6«o ljdfg:ynaf6 p8g\ ] jm| ddf l:y/ cj:yfaf6 wfjgdfud{ f pQ/ lbzflt/
u'8]sf] xjfOh{ xfh 40 s kl5 p8o\ f] . xjfOh{ xfh u8' b\ fsf] ;dfg k|ju] 0.75 m/s2 lyof] . pSt
xjfO{hxfh l7s hldgaf6 p8\g' k"j{sf] ult lx;fa ugx'{ f;] \ M
pbfx/0fdf xjfO{hxfhsf nflu lbOPsf] ljj/0f cg;' f/,
xjfO{hxfhsf] ;'?sf] ult -u_ = 0 (lsgsL l:y/ cj:yfaf6 lrq 7.7
u'8]sf]_
Psgf;n] ult kl/jtg{ ePsf] ;do (t) = 40 s
xjfO{hxfhsf] kj| ]u (a) = 0.75 m/s2
clGtd ult -v_ = ?
rfnsf] ;dLs/0f ko| f]u ubf,{
v = u + at
v = 0 + 0.75 × 40
v = 30 m/s pQ/ lbzftkm{
xjfOh{ xfh l7s hldgaf6 p8\g' kj" { 30 m/s pQ/ sf] ultn] ul' 8/x]sf] lyof] .
lj1fg tyf k|ljlwM sIff ( 101
2. l;wf /v] Lo rfnsf nflu ;?' sf] ult -u_, clGtd ult -v_, k|ju] -a_ / :yfgfGt/0f -s_
;DaGwL ;dLs/0f
dfgfF}, s'g} l;wf /v] Lo rfndf /x]sf] j:t' Ps :yfgaf6 csf{] :yfgdf :yfgfGt/0f -s_
eof] . :yfgfGt/0f xb'F f ;'?sf] ult -u_ Psgf;n] kl/jt{g xF'b} sx] L ;do -t_ kl5 lglZrt
clGtd ult -v_ kf| Kt u¥of] .
;dfg ¿kn] ult kl/jt{g eO/xs] f] cj:yfdf
:yfgfGt/0f = cf};t ult × ;do ;dLs/0f (i) cg';f/ t sf] dfg ;dLs/0f
(ii) df k|lt:yfkg ubf{ .
3. l;wf /v] Lo rfnsf nflu ;'?sf] ult -u_, ;do -t_, kj| u] -a_ / :yfgfGt/0f -s_ ;DaGwL
;dLs/0f
dfgf}F, sg' } l;wf /v] Lo rfndf /xs] f] j:t' ;dfg kj| ]u -a_ n] Ps :yfgaf6 csf]{ :yfgdf
:yfgfGt/0f -s_ eof] . k|ju] pTkGg x'Fbfsf] ;do -t_ df pSt j:tsf] ;'?sf] ult -u_
kl/jt{g eO{ clGtd ult -v_ aGof] .
;dLs/0f (ii) cg';f/,
;dLs/0f (i) af6 v sf] dfg /fVbf .
(iv) lj1fg tyf k|ljlwM sIff (
102
pbfx/0f 7.2
k"j{ klZrd /fhdfus{ f] 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/ u'l8;s]kl5 rfnsn] as|] sf] ko| f]u u/] . pSt df6] /;fOsnsf] ult
4 s ;Dd Psgf;n] 36b\ } 6 m/s2 sf] ultx|f; pTkGg eof] . ;'?sf] :yfgaf6 ePsf] df]6/;fOsnsf]
:yfgfGt/0f lx;fa ug'{xf;] \ M
pbfx/0fdf df6] /;fOsnsf nflu lbOPsf] ljj/0fcg;' f/,
klxnf] v08sf nflu bf;] f| ] v08sf nflu
;'?sf] ult -u_ = 0 ;'?sf] ult -u_ = klxnf] v08sf] clGtd ult = 20 m/s kj" {
kj| u] -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|ofu] ubf{, rfnsf] ;dLs/0f k|of]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{ lbzftkm{
s= 80-48
∴ s= 32 m kj"\ { lbzftkm{
;?' sf] :yfgaf6 ePsf] df]6/;fOsnsf] :yfgfGt/0f = klxnf] v08sf] :yfgfGt/0f + bf;] f| ]
v08sf] :yfgfGt/0f
= 400 + 32 = 432 m k\j" {
;Lwf /]vLo rfnsf nflu
v = u + at — (i)
v = u + v x t — (ii)
2
v2 = u2 + 2as — (iii)
s = ut + 1 at2 — (iv)
2
sg' } j:t' :jtGq ¿kdf k[YjLdf vl;/xs] f]
cj:yfdf xfjfsf] cj/fw] guGo dfGbf a = g /
s = h xG' 5 .
lj1fg tyf k|ljlwM sIff ( 103
l;wf /v] Lo rfnsf uf| km (Graph of linear motion)
:yfgfGt/0f ;do u|fkm -displacement- time graph_
;'/hn] cfk\mgf] ljBfnodf cfofh] gf ul/Psf] bf8} kl| tof]lutfdf bf8} sf] 6o« fsdf /fx] gnfO{
ljgoeGbf s]xL cufl8 b]v] . Ps}l5g kl5 ljgon] /fx] gnfO{ kl5 kf/] . tn lrq 7.8 / 7.9 df
b'j} hgf Psgf;n] cfcfkm\ gf] ultn] bu'bf{sf] ;donfO{ x- cIf -x-axis_ / :yfgfGt/0fnfO{ y- cIf
-y-axis_ df /fv]/ lvlrPsf] u|fkm lbOPsf] 5 .
lrq 7.8 bf}8sf] 6o« fsdf ljBfyL{ bub' {} lrq 7.9 bf}8sf] :yfgfGt/0f ;do uf| km
k|Zgx¿
1. dflysf] :yfgfGt/0f ;do u|fkmdf bv] fOPsf] sg' /]vfn] /f]xgsf] rfn / s'g /]vfn] ljgosf]
rfn hgfpF5 <
2. ;?' df /f]xg ljgoeGbf slt b'/Ln] cufl8 /xs] f lyP <
3. bf}8sf jm| ddf slt ;s]G8kl5 ljgon] /f]xgnfO{ lht5] g\ <
4, /]vf AB / CD dWo] sg' /]vfsf] es' fj -le/fnfk] gf_ a9L 5 < /]vfx¿sf] e'msfj /
;DalGwt JolStsf] ultlar s:tf] ;DaGw xG' 5 xf]nf <
u|fkm k|of]u u//] j:ts' f] rfnaf/] j0f{g ug{ ;lsG5 . sg' } j:ts' f] :yfgfGt/0f / ;DalGwt
:yfgfGt/0fsf nflu nfu]sf] ;dolarsf] ;DaGw b]vfpg] u|fkmnfO{ :yfgfGt/0f ;do uf| km
(s - t) elgG5 . :yfgfGt/0f ;do u|fkmdf ;donfO{ x - cIfdf / ;DalGwt :yfgfGt/0fnfO{ y -
cIfdf k|:t't ul/G5 . pSt uf| kmdf /]vfsf] e'msfjn] rfn cj:yfdf /x]sf] j:t'sf] ult hgfp5F .
b'Oc{ f]6f :yfgfGt/0f ;do /v] fx¿sf] em' sfjsf] tn' gf u/]/ l56f] jf l9nf] u'l8/x]sf] j:t' yfxf
kfpg ;lsG5 . t'ngfTds ¿kdf e'msfj a9L ePdf j:t'sf] ult klg a9L x'G5 / e'msfj sd
xbF' f ult klg sd x'G5 . bO' { /]vfx¿ sfl6Psf] :yfgdf j:t'sf] kf/ u/s] f] b/' L a/fa/ x'G5 .
104 lj1fg tyf k|ljlwM sIff (
ljm| ofsnfk 7.3
p2]Zo M j:td' f x'g] ult kl/jt{gsf] cjnfs] g ug{'
cfjZos ;fdu|L M Pp6f ;dtn ;tx ePsf] sl/a 3 m nfdf] sf7sf] kmns] , s]xL lstfax¿,
u'Rrf jf ;fgf] esG' 8f,] :6k jfr, rs jf kl] G;n, ?n/ jf 6k]
ljlw M
1. ljm| ofsnfk 7.2 nfO{ bfx] f]¥ofpgx' f];\ .
2. uR' rf jf esG' 8fn] ] kT| os] ;s] G] 8df kf/ u/s] f] :yfgfGt/0f gfkL tnsf] tflnsfdf egx{' f;] \ .
;do klxnf] ;]sG] 8 bf];f| ] ;s] ]G8 t;] f| ] ;s] G] 8 rf}yf] ;s] G] 8
:yfgfGt/0f ============== ============== ============== ==============
ult ============== ============== ============== ==============
3. kT| os] ;s] ]G8df uR' rf jf esG' 8f]sf] ult lx;fa ug'{xf];\ .
4. pSt tYofªs\ nfO{ lrq 7.10 df bv] fOP em} uf| kmdf k:| tt'
ug{x' f;] \ .
5. uf| kmdf lvlrPsf] /v] fsf] ems' fj lgDgfg;' f/ lx;fa ugx{' f];\ M
em' sfj = rlj9:fjtf/ = :yfgdf cfPsf] cGt/ (∆s) =… lrq 7.10 ;dfg ultn] u'l8/x]sf]
;dodf cfPsf] cGt/ (∆t)
h:t} M lrqdf b]vfOPsf] /]vfsf] nflu j:ts' f] lj:yfkg ;do u|fkm
e 'msfj = 82ms /s = 4m/s
5nkmn / lgisif{ M s-t uf| km /]vfsf] e'msfjn] j:ts' f] ult b]vfp5F .
pbfx/0f 7.3
tnsf] uf| kmdf Pp6f df]6/;fOsnsf] rfnnfO{ tLgcf]6f v08df bv] fOPsf] 5 . pSt v08df
df6] /;fOsnsf] cf;} t ult / ultsf] cj:yf klg n]Vgx' f];\ M
uf| kmcg;' f/, AB v08df
cf};t ult -VAB_ Ö :yfgfGt/0f ;do /]vfsf] em' sfj
Ö laGb' G (10, 200) / laGb' E (30, 600) larsf] e'msfj
lj1fg tyf k|ljlwM sIff ( 105
Ö ∆s Ö s –s Ö 600 – 200 Ö 400
∆t 21 30 – 10 20
t –t
21
VAB= 20 m/s
df6] /;fOsn cufl8 a9b\ } hfbF f
;do;uF } kf/ u/s] f] b'/L klg Psgf;n]
a9]sf] 5 . df]6/;fOsn ;dfg
ultn] -l;wf /]vfdf_ ul' 8/xs] f] 5 .
BC v08df cf;} t ult Ö 0 m/s, lrq g= 7.11
df]6/;fOsn l:y/ cj:yfdf /x]sf] 5 .
CD v08df cf;} t ult -VCD_ Ö :yfgfGt/0f ;do /]vfsf] e'msfj
Ö laGb' H (80,600) / laGb' J (120,200) larsf] em' sfj
Ö ∆s Ö s – s Ö 200 – 600 Ö – 400
∆t 2 – 1 120 – 80 40
t t1
2
VCD = –10 m/s
hxfF C0ffTds lrxg\ n] df]6/;fOsnsf] rfn ljk/Lt lbzfdf 5 cyft{ \ kms/]{ ;?' sf] :yfglt/
cfO/xs] f] eGg] hgfp5F . df]6/;fOsn k5fl8 kmls{bF} ubf{ a9]sf] ;do;Fu} Psgf;n] b/' L kf/ ub}{
kms]{sf] 5 . o; v08df klg df]6/;fOsn ;dfg ultn] u'l8/x]sf] 5 .
ljm| ofsnfk 7.4
lbOPsf] u|fkmn] Pp6f l;wf af6fdf Psgf;n] lxl“ 8/xs] f] dflg;nfO{ Pp6f ss' '/n] nv6] g\ vf]Hbf
10s ;dofjlwdf dflg;sf] rfnnfO{ bv] fOPsf] 5 . pSt dflg;sf] rfn j0f{g ug'x{ f;] \ . ;fyLx¿
;dx" df ldnL pSt rfn kb| zg{ ug{'xf];\ .
lrq g= 7.12 lj1fg tyf kl| jlwM sIff (
106
v08 AE v08 EH v08 HI
:yfgfGt/0f ;do /v] fsf] e'msfj :yfgfGt/0f ;do /]vfsf] sg' } bO' { =================
hg' ;'s} bO' { laGb'lar ;dfg laGb'df e'msfj km/s km/s
x- cIf;Fu ;dfgfGt/ :yfgfGt/0f ;do /v] fn] ;do a9b\ f klg j:ts' f] b'/L ga9]sf] cyft{ \ j:t'
l:y/ cj:yfdf /xs] f] 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 uf| kmdf jjm| /v] f ePdf rfn
cj:yfdf /xs] f] j:ts' f] ult c;dfg x'G5 .
lrq g= 7.13
ult – ;do uf| km (velocity- time graph)
ljm| ofsnfk 7.5
tn tflnsfdf lbOPsf tYofªs\ sf cfwf/df ;donfO{ x-cIfdf / ;DalGwt ultnfO{ y-cIfdf
/fvL 56' 6\ f56' 6\ } uf| km lvRgx' f;] \ .
tflnsf 01 2 3 45
l;wf /]vfdf ul' 8/x]sf df6] /;fOsnsf 55 5 5 55
nflu ;do (s)
ult (m/s)
lglZrt prfOaf6 :jtGq ¿kdf vl;/x]sf tflnsf
j:ts' f] nflu ;do (s) 0 1 2 3 4 5
ult (m/s) 0 9.8 19.6 29.4 39.2 49
p8\g ;?' u/]sf xjfO{hxfhsf nflu tflnsf
;do (s) 0 1 2 3 4 5
lj1fg tyf kl| jlwM sIff ( ult (m/s) 0 2 6 12 20 30
107
ca tkfOnF ] lvRg' ePsf] ult ;do u|fkmsf] cWoog u/L ljZni] f0f ug{'xf];\ .
u|fkm ult ;do /]vf ult ;do /v] f ljZn]if0f
cfsf/ em' sfj
klxnf] ================== ================== j:ts' f] ult -;dfg÷Psgf;n] kl/jtg{ , ========_=
bf;] |f] ================= ====================== ult ;do /v] fsf s'g} bO' { laGbl' arsf] em' sfj
-;dfg÷c;dfg_ ========
em' sfj / k|ju] sf] ;DaGw =======
t];f| ] ============ ==================== Psgf;n] ult kl/jtg{ xb'F f / c;dfg ¿kn]
ult kl/jt{g xb'F f e'msfjdf bl] vPsf] cGt/
==========
sg' } j:t'sf] ult / ;DalGwt ;dolarsf] ;DaGw bv] fpg] u|fkmnfO{ ult – ;do (v - t) u|fkm
elgG5 . o:tf] u|fkmsf] cjnfs] gaf6 j:t' l:y/ /xs] f,] ;dfg ultdf cufl8 a9s] f], /f]lsg
vf]hs] f] h:tf hfgsf/Lx¿ yfxf kfpg ;lsG5 . ult ;do u|fkmdf ;donfO{ x- cIfdf /
ultnfO{ y- cIfdf k:| tt' ul/G5 . ult ;do /v] fsf] em' sfjn] rfn cj:yfdf /xs] f] j:ts' f]
k|ju] hgfp5F . bO' c{ f6] f ult ;do /v] fx¿sf] e'msfjsf] tn' gf u//] ult kl/jt{gsf] b/df /xs] f]
leGgtfaf/] hfgsf/L kfpg ;lsG5 .
x- cIf;uF ;dfgfGt/ ult ;do /]vfn] ;do a9b\ f klg j:t'sf] ult kl/jt{g gePsf] cyf{t\
j:t' ;dfg ultn] ljgf k|ju] uO/xs] f] hgfp5F . e'msfj;lxtsf] l;wf ult–;do /]vfn] rfn
cj:yfdf /x]sf] j:t' ;dfg kj| u] n] uO/xs] f] hgfp5F . olb :yfgfGt/0f ;do u|fkmdf jjm| /v] f
ePdf rfn cj:yfdf /xs] f] j:ts' f] ult c;dfg xG' 5 .
ult v (m/s)
;do t (s) ;do t (s) ;do t (s)
;dfg ult :jtGq ¿kn] vl;/xs] f] j:t' c;dfg ult
lrq 7.14 lj1fg tyf kl| jlwM sIff (
108
ljm| ofsnfk 7.6 ult v (m/s)
lbOPsf] ult ;do u|fkmsf]
cWoog u/L tnsf] tflnsf k/" f
ug{'xf];\ .
;dfg kj| u] ePsf v08x¿dWo]
sg' v08df j:ts' f] ult tLj|
¿kn] kl/jtg{ ePsf] 5 <
;do t (s)
lrq 7.15
;dfg ultsf] v08 ;dfg k|j]usf] v08 c;dfg kj| u] sf] v08 ultxf| ;sf] v08
BC / ……
……. / …… ……./ …… ……. / ……
AB / GH v08x¿ dWo] GH v08df ult ;do /]vfsf] e'msfj AB v08df eGbf a9L 5 .
To;}n] pSt j:t'sf] ult GH v08df tLj| ¿kn] kl/jtg{ ePsf] yfxf kfpg ;lsG5 .
Ogl;o{ f -Inertia_
tn lbOPsf 36gfx¿df ;DalGwt tYo / sf/0f kQf nufpg 5nkmn ug'{xf];\ .
1. lkª v]Ng] jm| ddf o;nfO{ dRrfpg / dRrfP/ 5f]8]sf] lkª l:y/ cj:yfdf cfpg s]xL ;do
nfU5 .
2. l:jr cg ug]{ ljlQs} ljB't\ kª\vf hf8] n] 3D' bg} / 3'ld/x]sf] kª\vfsf] l:jr ckm ug]{
lalQs} /fl] sbF }g .
ha sg' } j:td' f nfUg] anx¿ ;Gtl' nt x'G5g,\ ToxfF j:ts' f] cj:yf -ult jf lbzf_ df sg' }
kl/jtg{ x'Fbg} . j:ts' f] cj:yf kl/jt{g xg' jf j:t' ;g{ pSt j:td' f c;Gt'lnt anx¿ nfUg'
kb{5 . j:tn' ] c;Gtl' nt ansf] k|ofu] af6 o;sf] cj:yfdf ug{ vfl] hg] kl/jt{gsf] cj/fw] u5{ .
c;Gtl' nt ansf] dfqf lgs} sd ePdf Ps} l5gdf l:y/ cj:yfdf ePsf] j:tn' fO{ 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 vfH] 5 / rfn cj:yfdf /xs] f] j:t' ;dfg ultn] pxL lbzfdf rfndf /xg vfH] 5 .
sg' } klg j:tn' ] 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 .
lj1fg tyf k|ljlwM sIff ( 109
lj|mofsnfk 7.7
Pp6f 6]a'ndf /flvPsf pl;g]sf] / gpl;gs] f] cG8fnfO{ 6]an' af6 3d' fpgx' f;] \ . 3l' d/xs] f]
cG8fnfO{ cfn}“ fn] 5f]P/ /fS] gx' f;] \ . /fl] sgf;fy cfn}“ f x6fpgx' f;] \ . ca s] x'G5 xg] {x' f;] \ .
cjnfs] g u/L k|fKt glthfnfO{ tnsf] tflnsfsf cfwf/df kl' i6 ug{'xf];\ .
cjnfs] g glthf JofVof
================= ================== ============
lk08 / Ogl;o{ flarsf] ;DaGw -Relation between mass and inertia_
lj|mofsnfk 7.8
p2Z] o M j:td' f lk08 / Ogl;{oflarsf] ;DaGw kb| z{g ug{'
cfjZos ;fduL| M p:t} bO' {cf]6f aft] n, 8f]/L, kfgL,
ljlw M
1. Pp6f af]tndf kfgL eg'{xf];\ / csf]n{ fO{ vfnL /fVgx' f];\ .
2. b'j}nfO{ ;dfg nDafO ePsf] 8f]/Ln] cufl8 k5fl8 rNg ;Sg] u/L sg' } cf8df
e'mG8o\ fpgx' f];\ .
3. ca e'mG8o\ fOPsf af]tnx¿nfO{ a/fa/ b/' L;Dd lj:yflkt u/L ;Fu} 5f]8g\ x' f;] \ /
ltgLx¿sf] rfnsf] cjnfs] g ugx{' f;] \ .
5nkmn / lgisif{ M sg' aft] n klxn] l:y/ cj:yfdf cfp5F < lsg xfn] f, 5nkmn ugx{' f;] \ .
cjnfs] g glthf JofVof
sd lk08 ePsfnfO{ /f]lsg nfu]sf] ;do Ö === === eGbf ==== klxn]
a9L lk08 ePsfnfO{ /f]lsg nfus] f] ;do Ö ==== /f]lsG5 .
sd lk08 ePsf] tyf a9L lk08 ePsf] bj' } j:t' oyfl:yltdf /xg vf]H5g\ . t;y{ ;a} j:t'df
Ogl;{of x'G5 . j:t'df xg' ] Ogl;{of o;sf] lk08df lge/{ x'G5 . j:t'sf] lk08 a9\bf Ogl;o{ f klg
a9\5 / lk08 36\bf Ogl;{of klg 365\ .
110 lj1fg tyf k|ljlwM sIff (
Ogl;o{ fsf lsl;d -Types of inertia_
!= l:y/ Ogl;{of -Inertia of rest_
lj|mofsnfk 7.8
p2Z] o M j:t'df x'g] l:y/ Ogl;o{ fsf] k|bzg{ ug{'
cfjZos ;fdu|L M l;Ssf, sfrF sf] lunf;, sf8{
ljlw
1. lrqdf h:t} lunf;sf] dfly sf8{ / To;sf] dfly l;Ssf lrq 7.16
/fVg'xf];\ .
2. sf8n{ fO{ PSsfl; tfGg'xf;] \ / s] x'G5, cjnfs] g ugx{' f];\ .
5nkmn / lgisif{ M l:y/ cj:yfdf /xs] f] l;SsfnfO{ PSsfl; rfndf Nofpg vf]Hbf o;n]
To;sf] cj/fw] u5{ . sf8{ PSsfl; rfndf cfPsf] x'gfn] l;Ssf rNg gkfpbF } of] l;Ssfaf6
6f9f hfG5 . h;n] ubf{ l;Ssf lunf;df v:5 .
sg' } l:y/ cj:yfdf /x]sf] j:ts' f] l:y/ cj:yfd} /lx/xg vf]Hg] u0' f l:y/ Ogl;o{ f xf] . l:y/
Ogl;{ofsf yk pbfx/0f tn k|:t't ul/Psf] 5 M
i. k|ofu] df /x]sf] sfk]{6nfO{ em' G8o\ fP/ lxsf{pbF f o;df ePsf] w'nf] em5{ .
ii. ?vdf cfFk kmn]sf] cj:yfdf o;sf] xfuF f xNnfpbF f cfkF v:5g\ .
iii. Sof/d v]Nbf uf]6Lx¿sf] rfªdf l:6fOs/n] hf8] n] lxsfP{ df s]jn lkFwsf] uf]6L lg:sG5 /
afsF L rfªF g9nLsg a:5 .
iv. a; PSsfl; rfndf cfpbF f To;leq /x]sf ofqx' ¿sf] z/L/sf] dflyNnf] efu l:y/
cj:yfd} /xg vf]H5 t/ a;sf] ;Dksd{ f /xs] f] z/L/sf] tNnf] efu eg] a;;uF }
rfndf cfp5F . h;n] ubf{ ofq'x¿ k5fl8lt/ xl' QG5g\ M
ljm| ofsnfk 7.9
sIffdf 5nkmnsf] lgisifa{ f6 dfly lbOPsf pbfx/0fx¿df pTkGg xg' ] Ogl;o{ fnfO{ tnsf]
tflnsfcg';f/ JofVof ugx'{ f;] \ .
pbfx/0f rfndf cfpg] efu jf l:y/ cj:yfdf /xg l:y/ Ogl;o{ fsf]
j:t' vfH] g] efu jf j:t' JofVof
============= =================== ====================== ==========================
lj1fg tyf kl| jlwM sIff ( 111
@= rfn Ogl;{of -Inertia of motion_
u'8b\ } u/]sf] ;fOsndf 7f]lsbF f 9'ªu\ fn] ;fOsnsf] ultnfO{ /fS] 5 / ;fOsn l:y/ cj:yfdf
cfpg vfH] 5 . ;fOsn rfnssf] z/L/ eg] klxns] } ultn] cufl8 uO/xg vfH] 5 . h;n]
ubf{ rfns cufl8lt/ xl' QG5 / eOF' 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;{of xf] . rfn Ogl;{ofsf
yk pbfx/0f tn k:| tt' ul/Psf] 5 M
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; a|]s nufpbF f o;df ePsf ofq'x¿sf]
z/L/ cufl8lt/ x'lQG5 .
iii. 8«fOe/n] 3D' tLx¿df a; PSsfl; df]8b\ f ofqx' ¿sf] z/L/ a; df8] ]sf] ljk/Lt lbzflt/
9lNsG5 .
iv. u'8\b} u/]sf] a;af6 embf{ ofq' e'OdF f k5fl/g] ;Defjgf x'G5 .
v. nª\u hDksf vn] f8Ln] nfdf] 5nfª nufpg sx] L b'/L bu'g]{ u5{g\ .
ljm| ofsnfk 7.10
sIffdf 5nkmnsf] lgisif{af6 dfly lbOPsf pbfx/0fx¿df pTkGg x'g] Ogl;o{ fnfO{ tnsf]
tflnsfcg';f/ JofVof ug{'xf;] \ .
pbfx/0f l:y/ cj:yfdf rfn cj:yfd} /xg rfn Ogl;o{ fsf]
cfpg] efu jf j:t' vfH] g] efu jf j:t' JofVof
================== ================== ====================== ============================
rfn;DaGwL Go'6gsf lgodx¿ -Newton's laws of motion_
;/ cfOHofs Go'6g -Sir Issac Newton_ Ps ef}ltszf:qL / ul0ft1 lyP . pgn] ;g\ 1687 df
j:ts' f] rfn;DaGwL tLgcf6] f lgod k|ltkfbg u/s] f lyP . Go'6gsf] rfn;DaGwL klxnf] lgodn]
ansf] kl/efiff lbG5 . bf;] f| ] lgodn] k|ofu] df ePsf] an / j:t'sf] lk08;uF kj| u] sf] ;DaGwsf]
j0f{g ub5{ . o;sf] ko| f]uaf6 ansf] dfkg ug{ ;lsG5 . Go'6gsf] t];|f] lgodn] ansf] u'0f
atfp5F .
112 lj1fg tyf kl| jlwM sIff (
Go'6gsf] rfn;DaGwL klxnf] lgod -Newton's first law of motion_
ljm| ofsnfk 7.11
5nkmnaf6 tnsf pbfx/0fx¿ h:t} bl} gs lj|mofsnfkx¿df j:t'sf] cj:yf kl/jt{g ug{ afxo\
kl/0ffTds ansf] cfjZostf pNnv] ug'{xf];\ .
klxnf] v08 -l:y/af6 rfn_ bf;] |f] v08 -lbzf kl/jt{g_ t];f| ] v08 -rfnaf6 l:y/_
!= d}bfgdf vn] f8Ln] km' 6an kf; ub{} v]Nbf
klxnf] v]nf8Lsf] uf8] fn] kx| f/ klxnf] v]nf8Ln] nufPsf] olb km' 6an / hldglar
ubf{ nfUg] kl/0ffTds ann] pSt ansf] lbzfdf k'm6an l;wf 3if{0f an pTkGg gePdf
ansf] lbzfdf km' 6an u'85\ . u8' ]/ hfG5 . csf]{ vn] f8Ln] km' 6an lg/Gt/ u'8\Yof,] h'g
nufPsf] kl/0ffTds ann] c;Dej xG' 5 . o;/L 3if0{ f
o;sf] lbzf kl/jt{g xG' 5 . tyf cGo v]nf8Ln] nufpg]
kl/0ffTds afx\o ann]
km' 6an l:y/ cj:yfdf
cfp5F .
@= afª\uf]l6ªu\ f] af6fdf a; u'8fpFbf
OlGhgn] nufpg] kl/0ffTds :6l] /ª x\jLn -steering wheel_ as|] tyf hldgl;tsf]
ansf] c;/ n] nufpg] kl/0ffTds ansf] 3if{0fn] nfUg] kl/0ffTds
c;/ ansf] c;/
=====================
================================ =================================
Go6' gn] rfn;DaGwL lgodx¿ kl| tkfbg ugk'{ j" { j1} flgs Uoflnlnof] UoflnnL -Galileo Galilei_
n] rfn;DaGwL Jojl:yt ¿kn] cWoog u/L Ogl;o{ fsf] lgod lbO;ss] f lyP . Go'6gn]
klg Ogl;{ofnfO{ kl/eflift ub}{ rfn;DaGwL klxnf] lgod kl| tkfbg u/s] f lyP . Go'6gsf]
rfn;DaGwL klxnf] lgodcg';f/ …s'g} c;Gt'lnt ansf] k|of]u gx'Ghn] ;Dd l:y/ cj:yfdf /x]sf]
j:t' l:y/ cj:yfd} /xG5 / rfn cj:yfdf ePsf] j:t' ;dfg ultn] pxL lbzfdf rln/xG5 .
o; lgodcg';f/ olb kl/0ffTds an -resultant force_ zG" o ePdf j:t' oyfl:yltdf /xG5 .
l:y/ cj:yfaf6 rfndf Nofpg / ;dfg ultn] u'l8/x]sf] j:t'nfO{ l:y/ cj:yfdf Nofpg
c;Gt'lnt an nfUgk' 5{ . t;y{ an egs] f] j:t'sf] cj:yf kl/jtg{ ug]{ sf/0f tŒj xf] . Go6' gsf]
klxnf] lgodn] c;Gt'lnt an gnfu'Ghn] l:y/ cj:yfdf /x]sf] j:t' l:y/ cj:yfd} /xg vfH] g]
/ rfn cj:yfdf /x]sf] j:t' rfn cj:yfd} /xg vf]Hg] u'0faf/] pNn]v 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] kZ| g M ;fOsnnfO{ l:y/ cj:yfaf6 rnfP/ ult kl/jt{g ub}{ rf8F f]rf8F f] u8' fpgk' g]{
cj:yfdf PSn} rfns / rfnssf] k5fl8 csf{] JolSt a:bf kj| ]udf s:tf] leGgtf cfpF5 <
;Dd k/s] f] Psgf;sf] af6fd] f klxnf] k6s ;fOsnsf] k]8ndf sd an nufP/ u8' fpFbf / bf;] |f]
k6s k8] ndf a9L an nufP/ u'8fpbF f pTkGg xg' ] k|ju] df s] leGgtf xG' 5 <
rfnsn] nufpg] an l:y/
ePdf, lk08 a9\bf k|ju]
36\5 . olb lk08 l:y/
ePsf] cj:yfdf ;fOsn
rfnsn] an a9fpg ;sd] f
lrq 7.17 ;fOsn rfns dfq x“'bfsf] lrq 7.18 ;fOsn rfns;u“ } k|ju] klg a9\5 .
k|ju] k5fl8 csf{] JolSt af]Sbfsf] kj| u]
dflysf] k|Zgdf ;fl] wP h:t} bl} gs hLjgdf nfu' xg' ] yk pbfx/0fx¿af/] 5nkmn ug'{xf];\ .
j:ts' f] lk08df x'g] kl/jt{gn] ubf{ j:t'df nufOPsf] ansf] 36a9n] k|ju] klg
k|j]udf klg kl/jt{g x'g] 36a9 x'g]
xfdLn] af]ss] f] ef/L la;fP/ l/Q} lx8F \bf rf8F f] df+zkz] Laf6 an a9L nufpFbf Ps} l5gdf
rf8F f] lx8F g\ ;lsG5 . tLj| ultn] bug' { ;lsG5 .
psfnfdf u8' b\ } u/s] f] 6«ssf] nf8] 36fpbF f ult ;jf/L ;fwgx¿df PS;n/6] /af6 OlGhgn]
kl/jtg{ rfF8f] rf8F f] x'G5 . nufpg] an a9fpbF f kj| ]u pTkGg x'G5 /
;fdfg nf]8 u/s] f] 7]nfuf8fnfO{ u8' fpgeGbf hf]8n] a|s] lyRbf tLj| ultx|f; x'G5 .
vfnL 7]nfuf8fnfO{ u8' fpg ;lhnf] x'G5 . v]n db} fgdf annfO{ rf8F f] u'8fpg a9L an
ko| f]u ug{k' 5{ .
dflysf pbfx/0fx¿df j:ts' f] lk08df x'g] kl/jtg{ tyf pSt j:td' f nufOPsf] andf xg' ]
kl/jtg{ n] j:ts' f] k|ju] df kg]{ c;/ bv] fOPsf] 5 . an / lk08;uF k|j]usf] ;DaGw cWoog ug{
tnsf] ljm| ofsnfk u/f}F .
lj|mofsnfk 7.12
p2Z] o M Go6' gsf] rfn;DaGwL bf;] f| ] lgod k|bzg{ ug{'
cfjZos ;fdu|L M 8foglds 6«nL jf vn] fg} f uf8L, SNofDk;lxtsf] lrq 7.19
Ps rSs] l3gL{, wfuf], tf}n em'G8o\ fpg] c+s'z, 50 g sf 10 cf6] f lj1fg tyf kl| jlwM sIff (
lk08x¿ -slotted masses_, 38L
114
ljlw M
1. lrqdf b]vfP em} pks/0fx¿nfO{ hf8] g\ 'xf];\ .
2. l3gLa{ f6 Ps ld6/ k/ 6]an' df lrxg\ nufpgx' f;] \ .
3. cs+ z' df 50 g lk08 /fvL 6«nLnfO{ 6]an' sf] lrxg\ dfly
/fVg'xf;] \ .
4. 6n« LnfO{ u'8g\ lbO{ 6]an' sf] csf]{ 5]p;Dd kU' g nfUg] ;do gfKg'xf;] \ / tnsf] tflnsfdf
egx{' f;] \ .
5. cs+ 'zdf csf]{ 50 g lk08 yKgx' f;] \ / :6]k 4 bfx] f]¥ofpg'xf;] \ .
6. j|mdzM cs+ 'zdf lk08x¿ yKb} :6k] 5 bfx] f]¥ofpg'xf;] \ .
6n« LnfO{ tfGg] an jf c+sz' df /flvPsf] :yfgfGt/0f ;do -t/s_ kj| u] -a = 2s/t2_
lk08sf] tf}n -W/N) -s/m_
========= 1 ======= =============
========= 1 ======= =============
tYofªs\ ljZn]if0f / glthf M 6«nLdf nufOPsf] an / k|j]usf] ;DaGwaf/] 5nkmn
ugx{' f;] \ .
tYofª\s ljZni] f0f / glthf M 6«nLdf /flvPsf] lk08 / kj| u] sf] ;DaGwaf/] 5nkmn ugx{' f;] \ .
5nkmn / lgisif{ M 6n« Lsf] lk08 l:y/ /fvL tfGg] an kl/jtg{ ubf{ 6«nLsf] kj| ]u a9\b} uof] .
To;u} /L tfGg] an l:y/ /fvL 6n« Ldf lk08 yKb} hfFbf kj| ]u 36b\ } uof] .
Go'6gsf] rfn;DaGwL bf];|f] lgodcg;' f/ …ansf] ko| fu] af6 sg' } j:t'df pTkGg x'g] kj| u] To;df
nfus] f] an;Fu ;dfgk' flts / To;sf] lk08;uF JoT' j|mdfg'kflts x'G5 .Ú
cyft{ \, sg' } j:td' f nfus] f] kl/0ffTds an a9fpbF f To;df pTkGg x'g] kj| u] klg a95\ .
k|ju] (a)∞F………………….( i) -lk08 l:y/ xF'bf_
j:t'df nfu]sf] kl/0ffTds an l:y/ ePsf] cj:yfdf o;sf] lk08 a9b\ } hfFbf kj| ]u 36\5 / lk08
36b\ f k|j]u a95\ .
k|j]u (a) ∞ 1/m………………..(ii) -an l:y/ x'bF f_
dflysf ;dLs/0f -i_ / -ii_ nfO{ ;o+ f]hg ubf,{
a ∞ F/m F ∞ ma
s'g} ;DaGwnfO{ ;dLs/0fsf ¿k lbgsf nflu To;df Ps cr/ /flz kl| ji6 ug{k' 5{ .
F = k ma……………..(iii) oxfF k|of]u ePsf] k cr/ /flz xf] .
lj1fg tyf k|ljlwM sIff ( 115
1 N ansf] kl/efiffcg;' f/, sg' } 1 kg lk08 ePsf] j:t'df 1 m/s2 sf] k|ju] pTkGg u/fpg k|ofu]
x'g] annfO{ 1 N elgG5 . ansf] dfg 1 N x'bF f ;dLs/0f (iii) df k sf] dfg klg 1 x'G5 .
\ F = ma
pbfx/0f 7.5
Pp6f 1500 kg lk08 ePsf] sf/ pQ/ lbzfdf 36 km/h sf] ultn] ul' 8/xs] f] lyof] . rfnsn]
o;sf] PS;n/6] / lyRbf 4 s kl5 ;dfg k|ju] n] 64 m k/ k'Uof] . pSt sf/df nfus] f] kl/0ffTds
an lx;fa ugx{' f;] \ . sf/df pTkGg k|ju] sf] lbzf pNn]v ug'x{ f;] \ .
oxfF,
sf/sf] lk08 (m) = 1500 kg
sf/sf] ;?' sf] 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 lrq 7.20
l;wf /]vLo rfnsf] ;dLs/0f k|of]u ubf,{
1
s = ut + at2
2
cyjf, 64 = 10 × 4 + 1 × a × 42
2
cyjf, 64 – 40 = 1 × a × 16
2
cyjf, 8a = 24
∴ a = 3 m/s2
Go6' gsf] rfn;DaGwL bf;] f| ] lgod k|ofu] ubf{, sf/df nfus] f] kl/0ffTds an
F=ma
F =1500 × 3 = 4500 N
t;y{ sf/df 4 s ;dfg k|j]u pTkGg xb'F f nfus] f] kl/0ffTds an 4500 N /x5] . sf/df
pTkGg k|j]usf] lbzf an nfus] f] lbzftk{m xG' 5 .
116 lj1fg tyf k|ljlwM sIff (
rfn;DaGwL Go6' gsf] t];|f] lgod (Newton's third law of motion)
k|Zg M s] lxF8\bf xfd|f] kt} nfn] hldgdf tnlt/ gbafOs{ g cufl8 a9\g ;S5f}F < Ps k6s sfl] ;;
u/L x]gx{' f;] \ .
ljm| ofsnfk 7.13
b'O{cf]6f Psgf;sf l:kª| t/fh'x¿ lng'xf;] \ . tn lrqdf b]vfOP h:t} l:k|ª\ t/fh' B sf] Pp6f
5]pnfO{ c8o\ fP/ /fVg'xf];\ / csf]{ 5]psf] cs+ 'zd] f l:kª| t/fh' A sf] c+sz' ] /fVg'xf;] \ . l:kª|
t/fh' A sf] csf]{ 5]paf6 lj:tf/} an nufP/ aflx/lt/ tfGg'xf;] \ . l:k|ª t/fh' A / l:kª| t/fh'
B n] b]vfpg] ansf] dfg / lbzf cjnf]sg ug{'xf;] \ .
lrqdf cjnfs] g glthf
l:k|ª t/fh' A n] l:k|ª t/fh' B
df nufPsf] an Ö
l:k|ª t/fh' B n] l:k|ª t/fh' A
df nufPsf] an Ö
lrq 7.21 Pp6 l:kª| t/fhn' ] csf{]nfO{ tfgs] f
lj|mof / k|ltljm| of bj' } slxNo} klg Pp6} B n] A nfO{ A A n] B nfO{ nufPsf] an
j:t'df nfUb}gg\ . Go'6gsf] rfn;DaGwL nufPsf] an
lgodcg';f/ s'g} j:t' A n] j:t' B df B
an nufof] eg] j:t' B n] klg j:t' A
df plQg} dfqfdf ljk/Lt lbzfdf an lrq 7.22 b'O{cf]6f anx¿ Pscfk;df
nufp5F . 7fl] sbf Pp6fn] csf{d] f nufpg] an
lrq 7.23 lrq 7.24
ljm| of / kl| tlj|mofdf a/fa/ kl/df0f / ljk/Lt lbzf eP tf klg Psn] csfn{ fO{ /2 ub{}g . ha
b'O{ a/fa/ / ljk/Lt an Pp6} j:td' f nfUb5g\ ta dfq kl/0ffTds an -resultant force_ z"Go
xG' 5 . ljm| of / kl| tlj|mof b'O{ km/s j:t' nfUg] ub5{ g\ . To;n} ] lj|mof / kl| tljm| ofdf Psn] csf{nfO{
/2 ug]{ x'Fbg} .
lj1fg tyf kl| jlwM sIff ( 117
ljm| ofsnfk 7.14
s'g} Ps j:t'n] bf;] f| ] j:td' f an nufp“bf bf];f| ] j:tn' ] klg klxnf] j:td' f ;f]xL dfg a/fa/ t/
l7s ljk/Lt lbzdf an nufp5“ . o;/L b'O{ j:tx' ¿df nfUg] hf8] L anx¿dWo] Pp6fnfO{ ljm| of
-action_ / csf]{nfO{ kl| tljm| of -reaction_ elgG5 . Go6' gsf] rfn ;DaGwL t;] |f] lgodcg';f/ ‘sg' }
klg ljm| ofsf nflu a/fa/ / ljk/Lt kl| tljm| of xG' 5 .’
xfd|f] jl/kl/ cjnf]sg ug{ ;lsg] j:tn' fO{ rfndf Nofpg ul/g] ljm| ofsnfkdf lj|mof / k|ltljm| of
56' o\ fpg'xf;] \ . h:t} M
pbfx/0f lrqdf ljm| of kl| tljm| of
8ª' \uf 8'ª\uf rfnsn] 8ª' \uf rfnsn] nufPsf]
lvofpbF f ug]{ ljm| of axfgfn] an af/a/sf] an kfgLn]
an nufP/ kfgLnfO{ nufpF5 / 8'ªu\ f cufl8
k5fl8 wsN] g] wsl] nG5 .
kfgLdf kf8} L kf}8L v]Ngn] ] kf8} L v]Ngn] ] nufPsf]
vN] bf ug{] ljm| of– xftn] an a/fa/sf] an kfgLn]
an nufP/ kfgLnfO{ xftdf nufpF5 / z/L/
annfO{ k5fl8 ws]Ng] . cufl8 xl' QG5 .
e'OF df pkmfbf{
========================== =======================
/s]6 k|R5k] 0f ========================== =======================
ubf{
r/f p8b\ f ========================== =======================
ufn] L xfGbf ========================== =======================
118 lj1fg tyf k|ljlwM sIff (
lj|mofsnfk 7.15
p2Z] o M Go'6gsf] t];|f] lgod k|bz{g ug{'
cfjZos ;fdu|L M an] g' , :6«, wfuf,] ;n] f6] k] , s}FrL
ljlw lrq 7.25 an] 'gsf] /s]6
1. an] 'gsf] ;txdf :6s« f] 6'j|mf 6k] n] 6f:F g'xf;] \ /
:6d« f wfuf] l5/fpg'xf;] \ .
2. lrqdf bv] fP h:t} u/L wfuf]sf bO' c{ f]6} 5]pnfO{ sg' } cf8df afWF g'xf];\ .
3. a]n'gdf xfjf eg'x{ f;] \ / o;sf] dv' xftn] RofKgx' f;] \ .
5. a]n'gsf] d'v PSsfl; 5f8] g\ x' f];\ / an] g' sf] rfn cjnf]sg ug{x' f];\ .
5nkmn / lgisif{ M Go6' gsf] rfn;DaGwL t;] f| ] lgodsf cfwf/df an] g' sf] rfnsf] j0fg{ ugx{' f;] \ .
Onfl:6l;6L / Knfl:6l;6L
tkfOFn] Onfl:6s zAb k9b\ f o;;Fu ;DaGwLt sg' sg' j:t' ;lDemg' xG' 5 < To:t}, Knfl:6s
eGgfn] sg' s'g j:t' ;Demg' x'G5, ;r" L agfpg'xf;] \ .
lj|mofsnfk 7.16
ansf] c;/
an nufp“bf ugk{' g{] ljm| of lrqdf cfsf/÷;fOhdf an x6fpb“ f kg' M dn"
kl/jt{g cj:yfdf cfpg] ÷gcfpg]
d]6\g] /a/sf b'O{ 5]paf6
RofKg,] tGsfpg,] aªU\ ofpg],
a6fg{]
/a/ aG] 8 tGsfpg] =============== ============== cfpg]
cfsf/ kl/jtg{ =============
xftsf cf}Fnfn] 6y' k:] 6 =================
lgrf{]g] ===================== ========================
Knfl:6ssf] 6j' m| fnfO{ bO' { =================
5]paf6 tGsfpg]
lj1fg tyf k|ljlwM sIff ( 119
xfjf e/]sf] a]ng' nfO{ b'O{ ================= ==================== =========================
xftsf] lardf /fvL lyRg] ===================
7f8f] kf/L /flvPsf]
l:6n l:k|ªnfO{ lj:tf/}
lyRg÷] tfGg]
/a/ AofG8nfO{ lj:tf/} tfGbf o;sf] nDafO a9\5 . o;df nufOPsf] afx\o an x6fpbF f of] cfˆgf]
dn" nDafOdf lkmtf{ cfpbF 5 . To:t} Pp6f /a/sf] an jf el/Psf] an] 'g lyRbf cfsf/ kl/jt{g
x'G5 / afXo an x6fpFbf kg' M cfk\mgf] jf:tljs cfsf/ k|fKt ub5{ .
sg' } j:td' f ljleGg lbzfaf6 an nufpFbf ;dud| f Psn ansf ¿kdf kl/0ffTds an -resultant
force_ sf] c;/ b]lvG5 . j:t'sf] agfj6, nufOPsf anx¿sf] kl/df0f tyf lbzfcg;' f/
kl/0ffTds ann] j:t'sf] cfsf/ / ;fOh kl/jtg{ ug{ ;S5 . kl/0ffTds an h;n] j:ts' f]
cfsf/ / ;fOhdf kl/jtg{ Nofp5F To;nfO{ l8kmldª{ an -deforming force_ elgG5 .
kZ| g M s] l:6n l:k|ªnfO{ 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 x6fpbF f
pSt j:t' cfˆgf] d"n l:yltdf lkmtf{ cfp5F .
s'g} l8kmdD{ 8 j:t'af6 l8kmld{ª annfO{ x6fpFbf
cfkm\ gf] d"n cj:yf kf| Kt ug]{ u0' f Onfl:6l;6L
xf] . tkfOF{n] of] kf7sf] ;'?df tof/ kf/s] f] ;r" L
Onfl:6l;6Lsf] kl/efiff;Fu dn] vfP gvfPsf]
hfrF ug'{xf;] \ .
agfj6sf cfwf/df j:t'x¿df km/s km/s lrq 7.26 Ps vDafdf cl8P/
Onfl:6l;6L xG' 5 . Onfl:6l;6L a9L xg' ] j:ts' f] /8x¿n] yfldPsf] s0ffn{ L kn'
cfsf/ / ;fOh kl/jtg{ ug{ ufx|f] x'G5 .
l:6nsf] Onfl:6l;6L Psbd} a9L xg' ] ePsfn]
o;sf] ko| fu] alnof] 3/, kn' , cflb lgdf{0fsf
nflu ul/G5 . j:td' f lglZrt kl/df0feGbf al9sf] l8kmld{ª\ d'5]sf] df6f]
an nufPdf pSt j:t' :yfoL ¿kdf l8kmd{ xG' 5 . o;/L
ansf] k|of]un] j:ts' f] cfsf/ / ;fOhdf :yfoL ?kn] kl/
jt{g cfpg] u'0fnfO{ Knfl:6l;6L elgG5 . Knfl:6l;6Ln] ubf{
d5' ]sf] df6fn] fO{ ;lhn} cfsf/ lbP/ O6F f agfpg ;lsG5 .
:yfoL ¿kn] l8kmd{D8 j:t'df lg/Gt/ an a9fpbF f r'Fl8g] jf
efFlrg] x'G5 .
120 lj1fg tyf kl| jlwM sIff (
5nkmn ug'{xf;] \ M
1= s] an nufpbF f tlGsPsf] b]lvg] j:tx' ¿ dfq Onfl:6s x'g\ <
2= Onfl:6s j:t'sf u0' fsf cfwf/df /a/ / l:6ndWo] sg' a9L Onfl:6s xG' 5 <
kl/ofh] gf sfo{
-s_ cfk\mgf] jl/kl/ pknAw ;fdu|Lx¿sf] k|ofu] u/L an] g' af6 rNg] v]nf}gf sf/ lgdf{0f ug'{xf;] \ .
pSt sf/df km/s km/s Onfl:6l;6L ePsf an] 'g / ljleGg tfn} x¿sf] k|of]uaf6 Go'6gsf]
rfn;DaGwL bf;] f| ] lgod k|bzg{ ug{'xf];\ .
-v_ :yfgLo ¿kdf pknAw ;fduL| x¿ / /a/ aG] 8sf] Onfl:6l;6Lsf] ko| fu] u/L Pp6f vn] f}gf
x]lnsfK] 6/ lgdf{0f ug{x' f];\ .
kl| tlaDag
1= :yfgfGt/0f ;do uf| km / ult ;do u|fkmsf] tn' gfTds cWoog
uf| kmdf bv] fOP u|fkmdf bv] fOP
u|fkm e'msfjsf] x-cIf ;u“ e}“m dflylt/ e}m“ em' sfj jjm| /]vf
dfg ;dfgfGt/ uPsf] l;wf tnlt/ uPsf]
/v] f l;wf /]vf
:yfgfGt/0f ult em' sfj zG" o, Psgf;sf] Psgf;sf] sg' } bO' {
;do /v] f j:t' l:y/ em' sfj, ;dfg em' sfj, ;dfg laGb'df
cj:yfdf ultn] cufl8 ultn] k5fl8 em' sfj
ult ;do k|ju] km/s km/s,
/v] f e'msfj z"Go, Psgf;sf] Psgf;sf] c;dfg ult
;dfg ult em' sfj, ;dfg em' sfj, ;dfg
k|j]u ultxf| ; s'g} bO' {
laGbd' f
e'msfj
km/s km/s,
c;dfg kj| u]
lj1fg tyf kl| jlwM sIff ( 121
2= l;wf /v] Lo rfn;DaGwL ul0ftLo ;d:of ;dfwfgsf nflu pkoS' t ;dLs/0fsf] 5gf]6
yfxf x'g'kg]{ r/ /flzx¿ t;] f]{ rfnsf nflu ;dLs/0f 7f8f] rfnsf nflu ;dLs/0f
;?' sf] ult -u_, clGtd ult v = u + gt
-v_, k|ju] -a_ / ;do -t_ dWo] v = u + at
s'g} tLgcf6] f
;'?sf] ult -u_, clGtd ult v2 = u2 + 2gh
-v_, kj| u] -a_ / :yfgfGt/0f -s_ v2 = u2+ 2as
dWo] sg' } tLgcf6] f
;'?sf] ult -u_, kj| ]u -a_ /
;do -t_ / :yfgfGt/0f -s_ dWo] 1 1
s = ut + at2 h = ut + gt2
s'g} tLgcf]6f 2
2
3= rfn;DaGwL Go6' gsf lgodx¿
klxnf] lgod bf];f| ] lgod t;] f| ] lgod
s'g} c;Gtl' nt ansf] ko| fu] gxG' h]n ansf] k|of]uaf6 sg' } j:td' f sg' } klg lj|mofsf
;Dd l:y/ cj:yfdf /x]sf] j:t' l:y/ pTkGg xg' ] kj| u] To;df nfu]sf] nflu a/fa/ /
cj:yf d} /xG5 / rfn cj:yfdf an;uF ;dfgk' flts / To;sf] ljk/Lt k|ltljm| of
ePsf] j:t' ;dfg ultn] pxL lbzfdf lk08;uF JoT' j|mdfgk' flts xG' 5 . x'G5 .
rfn cj:yfd} /lx/xG5 .
4= Onfl:6l;6L / Knfl:6l;6L
u0' f l8kmld{ª an x6fpb“ f cfsf/df xg' ] l/:6fl] /ª an
kl/jtg{ sf] lsl;d
Onfl:6l;6L klxn] s} cfsf/df cfpg] c:yfoL ljsl;t xg' ]
Knfl:6l;6L kl/jltt{ cfsf/ oyfjt\ /xg] :yfoL ljsl;t gx'g]
cEof; lj1fg tyf kl| jlwM sIff (
!= ;xL pQ/ 5fGg'xf;] \ M
-s_ ult ;do /]vfsf] em' sfjn] s]sf] dfg lbG5 <
-c_ ju] -cf_ ult
-O_ kj| ]u -O_{ :yfgfGt/0f
122
-v_ lbOPsf] ult ;do uf| km;Fu+ ;DalGwt :yfgfGt/0f ;do uf| km sg' xf] < V t
-c_ -cf_ -O_ -O_{
-u_ u8' b\ } u/]sf] a;af6 cfn] g{ ' hf]lvdk"0f{ x'G5 . o; egfOnfO{ s'g cfwf/df kl' i6 ug{
;lsG5 <
-c_ l:y/ Ogl;{of -cf_ rfn Ogl;{of
-O_ rfn;DaGwL bf];f| ] lgod -O_{ rfn;DaGwL t;] f| ] lgod
-3_ lj|mof / kl| tlj|mofsf ;Gbed{ f sg' egfO ;xL x'G5 <
-c_ Psn] csf{n] fO{ /2 ug{ ;S5g\ . -cf_ b'j} Pp6} j:t'df nfU5g\ .
-O_ a/fa/ t/ pxL lbzfdf nfU5g\ . -O{_ bO' { 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_ ldr]sf] lk7fn] fO{ /f]6Lsf] cfsf/ lbg'
-O{_ Aof8\ldG6gsf] ¥ofs]6n] ss xfGg'
-r_ ;8sdf ;dfg ultn] ul' 8/xs] f dfnafxs 6s« / sf/df ;dfg an nufpg ;Sg]
as|] sf] k|ofu] u/L /fl] sPdf tnsf dWo] s'g egfO ;xL x'G5 <
-c_ 6s« n] kf/ ug]{ b/' L sf/n] kf/ ug]{ b/' LeGbf sd x'G5 .
-cf_ sf/n] kf/ ug{] b/' L 6«sn] kf/ ug]{ b'/LeGbf sd xG' 5 .
-O_ 6s« n] kf/ ug]{ b'/L sf/n] kf/ ug]{ b/' L ;dfg x'G5 .
-O_{ 6s« n] kf/ ug]{ b/' L sf/n] kf/ ug{] b'/L ;u+ ;DaGwLt xFb' }g .
@= km/s nV] g'xf;] \ M 123
-s_ :yfgfGt/0f ;do u|fkm / ult ;do u|fkm
-v_ l:y/ Ogl;o{ f / rfn Ogl;o{ f
-u_ Onfl:6l;6L / Knfl:6l;6L
lj1fg tyf kl| jlwM sIff (
#= sf/0f n]Vgx' f];\ M
-s_ ;dfg ultn] ul' 8/x]sf df]6/;fOsn, sf/, 6«s, a;, 6]«g cflbnfO{ l:y/ cj:yfdf
Nofpg km/s km/s ;do nfU5 .
-v_ ?v xNnfpbF f kft tyf kmn v:5g\ .
-u_ a; ofqfsf j|mddf ofqn' ] cfk\mgf] l;6;+Fu} eOF' df /fv]sf] emf]nf a; rn]sf] s]xL ;do
kl5 cufl8sf] l;6glhs ku' s] f] e]6] .
-3_ aGb'saf6 ufn] L 5f]8\bf o;nfO{ bl/nf] cf8 lbgk' 5{ .
-ª_ bO' {cf6] f ;dfg cfsf/ ePsf /a/sf annfO{ ;F+u} eO' {dF f v;fNbf Pp6f a9L plk|mPsf]
kfOof] .
-r_ /a/ aG] 8nfO{ lglZrt ;LdfeGbf a9L tGsfpg' xFb' g} .
$= tnsf kZ| gsf] pQ/ n]Vgx' f];\ M
-s_ cf;} t ult / k|j]usf] kl/efiff n]Vg'xf;] \ .
-v_ l;wf /v] Lo rfnsf lgDglnlvt ;dLs/0fx¿ kd| fl0ft ug{'xf;] \ .
-c_ v = u + at
-cf_ v2 = u2 + 2as
O_ s = ut + 1 at2
2
-u_ l;wf /]vLo rfndf ;dfg ultn] ul' 8/x]sf] j:t'sf] rfn b]vfpg Ps Pscf6] f
:yfgfGt/0f ;do u|fkm / ult ;do u|fkm 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] k|s[lt pNnv] ugx'{ f];\ .
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_ ;+Fus} f] :yfgfGt/0f
;do u|fkmdf v/fof]
/ s5'jfsf] bf8} af/]
syfdf v/fof] / :yfgfGt/0f s(m)
s5j' fsf] rfnnfO{
Ps l;wf /v] Lo
rfnsf ¿kdf kb| zg{
ul/Psf] 5 . pSt
u|fkmsf] cjnf]sg
u/L bf8} sf] ;?' cftb] ;do t(s)
lv clGtd;Dd v/fof] / s5'jfsf] bf8} ljm| of ;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/0f nV] gx' f;] \ .
-5_ lk08 / Ogl;o{ flarsf] ;DaGw n]Vg'xf];\ .
-h_ rfn;DaGwL Go'6gsf] klxnf] lgod nV] g'xf;] \ .
-em_ kl/0ffTds ann] j:t'sf] cj:yf abN5 egL b]vfpg bO' c{ f]6f pbfx/0f nV] gx' f;] \ .
-`_ tLj| ult / Go6' gsf] rfn;DaGwL klxnf] lgodsf cfwf/df kxf8sf 3'DtLx¿df x'g
;Sg] a; b'36{ gfaf/] JofVof ug{'xf];\ .
-6_ rfn;DaGwL Go6' gsf] bf];|f] lgod nv] L F = ma k|dfl0ft ug{'xf];\ .
-7_ rfn;DaGwL Go'6gsf] t];|f] lgod nV] g'xf;] \ .
-8_ bl} gs hLjgdf Go6' gsf rfn;DaGwL tLgcf]6} lgoddf cfwfl/t lj|mofsnfksf bO' {
b'Oc{ f]6f pbfx/0fx¿ nV] gx' f];\ .
-9_ Go'6gsf rfn;DaGwL klxnf], bf;] |f] / t];f| ] lgodsf s'g} bO' { b'O{cf6] f pkofu]
vf]hL u/L ltgsf] JofVof ugx{' f;] \ .
ljm| ofsnfk pkofu] x'g] rfn;DaGwL JofVof
===================== Go6' gsf] lgod
==================== ========================
lj1fg tyf kl| jlwM sIff ( 125
-0f_ tn lrqdf b]vfOPsf ljm| ofsnfkdf ljm| of / k|ltljm| of 56' o\ fpgx' f];\ .
-t_ pbfx/0f;lxt Onfl:6l;6L / Knfl:6l;6L kl/eflift ugx{' f];\ .
ul0ftLo ;d:ofx¿
-s_ l:y/ cj:yfaf6 wfjg dfu{df blIf0f lbzftkm{ u8' g\ ;'? u/]sf] xjfOh{ xfhdf 1.5 m/s2
sf] ;dfg kj| u] pTkGg eof] / 30 s kl5 hldgaf6 p8o\ f] . xjfO{hxfh wfjgdfu{df u8' \
bf ;?' sf] :yfgaf6 clGtd :yfg ;Ddsf] :yfgfGt/0f / l7s hldgaf6 p8\g' k"js{ f] ult
lx;fa ugx{' f;] \ . (675 m blIf0f, 45 m/s blIf0f_
-v_ /f]xgn] Pp6f kn' sf] dflyaf6 gbLsf] kfgLdf 9ª' \uf v;fn] / ;'/hn] tn glbsf] 5p] df a;L
:6kjfrsf] ;xfotfn] 9ª' \ufnfO{ kfgLsf] ;tx;Dd cfOk'Ug nfu]sf] ;do 2 s kQf nufP .
9'ª\ufsf] v;fOdf k|j]unfO{ 9.8 m/s2 dfgL kfgLsf] ;txaf6 kn' sf] prfO lx;fa ug{x' f;] \ .
(19.6 m)
-u_ ;/' hsf] lk08 50 kg / pgn] r9s] f] ;fOsnsf] lk08 12 kg /x]sf] 5 . pgn] cf/] fnf] af6f]
df ;fOsn u'8fpbF f 2 m/s2 sf] k|ju] pTkGg eof] . pSt cj:yfdf ;fOsndf nfu]sf]
kl/0ffTds an lx;fa ug{x' f;] \ . (124N)
-3_ Pp6f 1500 kg lk08 ePsf] sf/ 72 km/h sf] ultn] ul' 8/xs] f] lyof] . rfnsn] a]s| sf] ko| f]
u ubf{ 50 m b/' L kf/ u/]kl5 To;sf] ult 10 km/h eof] . pSt cjlwdf sf/df nfus] f]
kl/0ffTds an lx;fa ug'x{ f];\ . (5850 N )
-ª_ ;Fu}sf] lrqdf Pp6f a;sf] rfnnfO{ ult ;do uf| kmdf bv] fOPsf] 5 . u|fkmsf] cWoog u/L
tnsf k|Zgx¿sf] pQ/ n]Vg'xf];\ .
-c_ ;dfg ult, ;dfg k|j]u, c;dfg :yfgfGt/0f (m)
k|ju] / ultxf| ;sf v08x¿ 5'66\ ofP/
nV] g'xf;] \ .
-cf_ ;dfg kj| ]u ePsf v08x¿dWo] sg'
v08df j:ts' f] ult tLj| ¿kn]
kl/jtg{ ePsf] /x5] <
-O_ C / D sf] lardf a;sf] kj| u] sf] dfg
slt 5 < ;do (s)
-O{_ a;n] C af6 D df k'Ubf x'g] :yfgfGt/0f lx;fa ug'{xf];\ . -70 m k"j{ tkm{ _
126 lj1fg tyf kl| jlwM sIff (
* ;/n oGq
(Simple Machine)
ljm| ofsnfk 8.1
tnsf lrqx¿ cjnfs] g u/L tflnsf k"/f ug{x' f];\ M
;/n oGq
ul/Psf
sfo{
ko| fu]
ePsf]
;/n oGq
lrq 8.1
b}lgs hLjgdf ul/g] ljleGg lsl;dsf sfon{ fO{ ;xh agfpg w]/} ks| f/sf cfh} f/sf]
k|of]u ul/G5 . k]rs;, l3gL{, kfªu\ f| / la8F , lrD6f, df6] / prfNg] Hofs, xlF ;of, aGr/f] cflb
3/fo;L sfod{ f ko| fu] xg' ] cf}hf/x¿ xg' \ . oL cfh} f/ k|ofu] ug{ lahn' L, l8hn] jf k]6f« n] sf]
cfjZostf kbg{} . dfgjLo ann] dfq ;~rfng ug{ ;lsG5 . o;/L xfd|f sfo{nfO{ ;lhnf,]
l56f] / ;'ljwfhgs 9ª\un] ;DkGg ug{ ko| f]u ul/g] ;fwf/0f agfj6 ePsf pks/0fnfO{ ;/n
oGq elgG5 . agfj6sf cfwf/df ;/n oGq rf/ ks| f/sf xG' 5g\, tL x'g,\ pQf]ns -lever_, l3gL{
-pulley_, kfªu\ |f / laF8 -wheel and axle_,
58s\ ] ;tx -inclined plane_ . kr] -screw_ 400 N
/ km;] f] -wedge eg] 58\s] ;txs} ljlzi6
¿k xg' \ . 600 N 10 m
5m
;/n oGqsf] ko| f]un] an j[l4 ug{ ;lsG5 .
lrq 8.2 df pQf]nssf] ko| f]u u/L sfo{
ubf{ 400 N an nufP/ 600 N sf] nf]8nfO{ lrq 8.2 pQf]nssf] ko| f]un] nf8] prflnPsf]
lj1fg tyf kl| jlwM sIff ( 127
p7fOPsf] 5 . cyf{t\ nf]8 prfNg ko| f]u ePsf] ansf] 1.5 u0' ff a9L nf8] p7fOPsf] 5 . s'g}
klg ;/n oGq k|of]u u/L sfo{ ubf{ nf]8 / Okmf]6s{ f] cg'kft g} oflGqs kmfObf xf] . cyft{ \
ofl Gqs km fObf (M A) = Onkf8]mf]6({ L(Eoaffdo)rt)
oflGqs kmfObf bO' c{ f]6f ansf] cg'kft ePsfn] o;sf] s'g} PsfO xFb' g} .
s'g} klg ;/n oGqdf Okmf{]6sf] ult (Velocity of effort) / nf]8sf] ult (Velocity of load) sf]
cgk' ftnfO{ ;/n oGqsf] ult cg'kft elgG5 .
cyft{ \
u lt c g'kft (VR ) = Okmf]6{sf] ult
nf]8sf] ult
b'/L kf/ ug{ nf8] / Okmf6{] nfO{ a/fa/ ;do nfUg] ePsfn],
ult cg'kft (VR) = Okmf6{] n] kf/ u/s] f] b/' L Okmf6{] n] kf/ u/s] f] b'/L = Okmf6{] b/' L÷nf]8 b/' L
;do
x'G5 . nf8] n] kf/ u/]sf] b'/L
lrq 8.2 sf] pQf]nsdf ann] kf/ ug]{ b/' L tf}nn] kf/ ug{] b'/Lsf] 2 u'0ff 5 . o;n] pSt
pQf]nssf] ult cgk' ft lbG5 .
ult cg'kft b'Oc{ f6] f ultsf] cgk' ft ePsfn] o;sf] s'g} PsfO xbF' }g .
dfly pNnv] ePsf ;q" x¿sf] k|ofu] af6 ;a} k|sf/sf ;/n oGqsf nflu oflGqs kmfObf / ult
cg'kft kQf nufpg ;lsG5 .
1. l3gL{ (Pulley)
l3gLs{ f] ko| f]u gu/L emG8f]Qfn] g ubf{ 8f/] Ldf nufOPsf] ansf] lbzf dflylt/ xG' 5 t/ l3gL{sf]
ko| fu] ubf{ an tnlt/ nufOG5 . oxfF l3gLn{ ] ansf] lbzf kl/jtg{ u/]/ sfdnfO{ ;lhnf]
agfOlbPsf] xG' 5 . l3gL{ Ps k|sf/sf] ;/n oGq xf] . cfˆgf] cIfdf :jtGq ¿kdf 3D' g ;Sg]
sf7, Knfl:6s jf wft'af6 ag]sf] uf]nf] 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{] 5]pdf an -effort_
nufOG5 . l3gL{sf] ko| f]u ljleGg 7fpdF f ul/G5, h:t} M Ogf/af6 kfgL tfGg, 7n' f 7n' f
ejgx¿ agfpbF f lgdf0{ f ;fduL| dflyNnf] tnfdf nh} fg cflb .
128 lj1fg tyf kl| jlwM sIff (
ljm| ofsnfk 8.2
lrqdf bv] fP h:t} u/L Ps rSs] crn
l3gL,{ Ps rSs] rn l3gL{ / ;+o'St
l3gL{ h8fg ug{x' f;] \ . sdfgL t/fh'
-spring balance_ sf] k|of]u u/L k|To]s
l3gL{ k0| ffnLdf kfnk} fnf] lbPsf] nf]8
prfNgx' f;] \ . nf8] nfO{ 20 cm dfly p7fpg crn l3gL{ rn l3gL{ ;+o'St l3gL{
Okmf] 6{nfO{ slt b/' L;Dd tfGg' k¥of] :s]nn]
lrq 8.3
gfk/] kQf nufpgx' f];\ . o; ljm| ofsnfkaf6
cfjZos tYofªs\ x¿ ;ªs\ ng u/L tnsf] h:t} tflnsfdf egx{' f;] \ .
gf]6 M Okmf6] n{ ] kf/ u/s] f] b/' L -effort distance_ eGgfn] 8f]/L ;?' sf] :yfgaf6 slt 6f9f k'Uof]
eGg] hgfpF5 . nf]8n] kf/ u/s] f] b'/L -load distance_ eGgfn] nf]8 ;?' sf] cj:yfaf6 slt
dfly p7o\ f] 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/ ÖOkmf]6{ × O=b' nf]8 × nf]=b'
5nkmn tyf lg:sif{ M
tYofª\ssf cfwf/df lx;fa ugx{' f;] \ / ;fl] wPsf kZ| gx¿ xn ug{x' f];\ .
-c_ klxnf] lrqdf bv] fOPsf] l3gL{ / bf];f| ] lrqdf b]vfOPsf] l3gLd{ f s] leGgtf 5 <
-cf_ Okmf6] { b'/L / nf8] b/' Lsf] cgk' ft / l3gLs{ f] ;ªV\ oflar s] ;DaGw 5 <
-O_ sg' l3gL{ ;dx" df nf8] / Okmf6] s{ f] cg'kft ;a}eGbf sd / s'gdf ;ae} Gbf a9L 5 <
-O{_ o:tf l3gL{x¿ sg' s'g 7fpFdf ko| f]u u/]sf] b]Vge' Psf] 5 <
l3gL{ k|0ffnL crn, rn / ;o+ S' t u/L tLg k|sf/sf x'G5g . sg' } lglZrt 7fpF df l:y/ /x/] 3'Dg]
l3gL{nfO{ crn l3gL{ elgG5 . o;nfO{ ansf] lbzf kl/jtg{ ug{ k|ofu] ul/G5 . tf}n;Fu} :yfg
kl/jt{g x'g] l3gL{nfO{ rn l3gL{ elgG5 . rn l3gL{n] ansf] lbzf kl/jtg{ ug{ ;Sbg} . rn
/ crn b'j} ks| f/sf rSsfx¿ ePsf] l3gL{nfO{ ;+oS' t l3gL{ elgG5 . ;+oS' t l3gLd{ f sDtLdf
Pp6f rn / Pp6f crn rSsfx¿ x'G5g\ . rSsfx¿sf] ;ª\Vof a9fpFb} nh} fbF f l3gLn{ ] ug]{ sfd
j|mdzM sd ann] ug{ ;lsG5 . sd ann] w]/} sfd xg' 'nfO{ lskmfotL xg' ' elgG5 . t;y{ w]/}
rSsf ePsf l3gLx{ ¿ a9L lskmfotL xG' 5g\ .
lj1fg tyf kl| jlwM sIff ( 129
ult cg'kft (Velocity ratio) height 2m rope efforts height from
moves the pully
Psn rn l3gL{df nf]8n] kf/ ug{] b/' LeGbf from the load to 2m to celling
pully to moves is 1m
to 1m
Okmf6] {n] kf/ ug]{ b'/L bfA] a/ xg' ] ePsfn] celling is
2m
ult cg'kft 2 xG' 5 . o;df nf]8nfO{
8f/] Lsf bO' { v08n] yfds] f] x'G5 .
lrq 8.4 Psn rn l3gLd{ f an b/' L / tfn} b/' L
lj|mofsnfk 8.2 af6 kf| Kt lgisifc{ g;' f/ Ps rSs] crn l3gLd{ f nf8] n] kf/ ug]{ b/' L / Okmf]6n{ ]
kf/ ug{] b/' L a/fa/ x'g] ePsfn] ult cg'kft 1 xG' 5 . o;df eg] 8f]/Lsf] Ps v08n] dfq nf]8
yfd]sf] x'G5 . t;y{
ult cg'kft (VR) = nf8] nfO{ yfDg k|of]u ul/g] 8f]/Lsf] v08sf] ;ª\Vof x'G5 .
oflGqs kmfObf (Mechanical Advantage)
nf8] / Okmf6] {sf] cgk' ftn] oflGqs kmfObfsf] dfg lbG5 . ljm| ofsnfk 8.2 af6 k|fKt lgisif{cg;' f/
l3gL{ k|0ffnLdf l3gLs{ f] ;ª\Vof a9b\ } hfbF f oflGqs kmfObf klg a9\b} hfG5 . l3gLs{ f] nflu,
oflGqs kmfObf (MA) = nf8] (Load)
Okmf6]{ (Effort)
pbfx/0fsf nflu l3gL{ ko| f]u u//] 200N sf] tf}n p7fpg 50N sf] an nufpg' k¥of] eg] o;af6
xg' ] oflGqs kmfObf (Mechanical Advantage) MA = 200N = 4 x'G5 .
50 N
o;sf] cy{ pSt l3gLs{ f] ko| fu] ubf{ 50N sf] ann] 4 u'0ff a9L tfn} p7fpg ;lsG5 .
Psn crn l3gL{df 3if{0f guGo ePdf nf]8 Spring balance
/ Okmf6] { a/fa/ x'G5 . t;y{ oflGqs kmfObf
;fdfGotof Ps x'G5 t/ 3if0{ fn] ubf{ l3gLd{ f weight 60 cm
nufpg] an tfn} eGbf a9L xg' klg ;S5 . o:tf]
cj:yfdf o;sf] oflGqs kmfObf PseGbf sd lrq 8.5 58\s] ;tx
x'G5 . oflGqs kmfObf Ps jf PseGbf sd eP
tfklg o;n] ansf] lbzf kl/jt{g ub5{ . nf]8nfO{
;f]em} dfly prfNg'eGbf l3gL{ ko| f]u u/L annfO{ tnlt/ nufP/ nf]8dfly prfNg ;lhnf] xG' 5 .
130 lj1fg tyf k|ljlwM sIff (
2. 58s\ ] ;tx (Inclined plane)
lj|mofsnfk 8.3
km/s km/s ;txsf] nDafO ePsf jm| dzM 200 cm, 300 cm / 400 cm t];f]{ kmn]s
lng'xf;] \ . tL kmns] nfO{ 60 cm hlt cUnf] 7fp“df 58s\ ] kf/L /fVg'xf];\ . Pp6f
kmns] sf] ;tx;u“ 3if{0f Psbd} Gog" x'g] lrKnf] ;tx ePsf] sf7sf] ;fgf] Ans lngx' f;] \ .
pSt AnsnfO{ kfn}kfnf] sdfgL t/fh'sf] k|ofu] u/L tLgcf]6} 58\s] ;txx¿ dfly tfGbf nfUg]
ansf] tYofªs\ ;ªs\ ng ug'{xf];\ . k|fKt tYofª\snfO{ tnsf] tflnsfdf egx'{ f;] \ / cfjZos
kl/df0fx¿sf] lx;fa ugx'{ f;] \ .
j|m=;= 58s] ;tx 58s] ;tx Uflt Nff8] Okmf]6{ oflGqs sfo{Ifdtf
nDafO (l/cm) prfO (h/cm) cgk' ft kmfObf
1. 200 60
2. 300 60
3. 400 60
5nkmnsf nflu kZ| gx¿
1. 6s« af6 ;fdfg /fVbf -nf8] ubf_{ / emfbf{ B
-cgnf8] ubf_{ t;] f{] kmns] lsg ko| fu] ul/G5 <
2. Psbd} 7f8f] vfnsf] -em' sfj sd ePsf_] H
e¥ofª / e'msfj a9L ePsf] e¥ofªdWo] sg' df l
plSng ;lhnf] xG' 5, lsg <
3. kxf8sf] 3d' fp/f] af6fsf] kmfObf s] xf] < A lrq 8.6 58s\ ] ;tx
6s« df ufx|f}F ;fdfgx¿ /fVg jf emfgs{ f nflu
58s\ ] agfP/ kmns] k|of]u ul/G5 . 58\s]
kmn]saf6 ;fdfgnfO{ u'8fP/ ;lhn} /fVg tyf emfg{ ;lsG5 . sg' } ufxf| F} ef/nfO{ cUnf]
7fpdF f ;lhn} k'¥ofpg ko| f]u ul/g] le/fnf] ;tx ePsf] pks/0fnfO{ 58s\ ] ;tx (Inclined
plane) elgG5 .
;u}sF f] lrqdf 58s\ ] ;txdf 58s\ ] nDafO -AB=l_ n] Okmf6] {n] kf/ u/]sf] b/' L / 58s\ ]
;txsf] prfO -BC=h_ n] nf8] n] kf/ u/s] f] b'/L hgfp5F . t;y{ 58\s] ;txsf nflu
Okmf6] { b'/L
ult cg'kft = nf]8 b/' L
58s\ ] ;txsf] nDafO
= 58s\ ] ;txsf] prfO
VR = l / h 131
lj1fg tyf kl| jlwM sIff (
prfOnfO{ oyfjt\ /fvL 58s\ ] ;txsf] 300 450 600
nDafO a9fpFbf o;n] ;tx;Fu agfpg] sf0] f
36b\ } hfG5 . 58\s] ;txsf] nDafOnfO{ hlt
nfdf] agfof] Tolt g} an b'/L a9\5 . h;n]
ubf{ ;/n oGqn] k|jw{g ug]{ an a95\ / lrq 8.7 ;dfg prfO t/ km/s km/s le/fnf]kg
sfo{ ug{ ;lhnf] x'G5 . 58s\ ] ;txdf o;sf] ePsf 58s\ ] ;tx
prfOnfO{ oyfjt\ /fvL ;txsf] nDafO
a9fpbF } nfFbf ult cgk' ft / oflGqs kmfObf a9\5 . kxf8sf]
le/fnf] hldgdf lgdf0{ f xg' ] ;8sx¿df w/] } 3D' tLx¿ /fvL
;8ssf] nDafO a9fOPsf] xG' 5 . h;n] ubf{ psfnfdf
uf8Lx¿sf] OlGhg -engine_ af6 nfUg] ann] ef/L tf}nnfO{
;lhn} tfGg ;S5 .
2 -s_ km] ;f] (Wedge) lrq 8.8
b}lgs hLjgdf rSs'sf] k|of]un] kmnk"mn sf6\g,] r'n];Ln] height distance dravelled
by the efforts
t/sf/L sf6g\ ], aGr/fn] bfp/f lrg]{ cflb sfo{ u/s] f] cjnf]sg of
wedge
ug{ ;lsG5 . oL sfo{x¿df k|of]u ePsf pks/0fx¿ km] ;fs] f
pbfx/0fx¿ xg' \ . logdf x'g] wf/ bO' {cf6] f 58\s] ;tx ldn/]
ag]sf] x'G5 . o;/L Psflt/ df6] f] / km/flsnf] efu ePsf] /
csfl{] t/ b'j} 58\s] :ftx ;fF3'/f] xb'F } wfl/nf] ags] f] pks/0f distance dravelled
km] ;f] xf] . of] 58s\ ] ;txsf] l;4fGtdf ags] f] x'G5 . To;} by the load
n] o;nfO{ 58\s] ;txsf] ljlzi6 ¿k dflgG5 . lrq 8.13
lrq 8.9 km] ;f]
df k]m;f] j:t'leq l5/]sf] cj:yfdf o;sf] rf8} fO a/fa/sf] efudf 3if{0f pTkGg xg' ] ePsfn]
pSt rf8} fO nf]8 b/' L x'G5 . To:t} j:tl' eq km] ;f] ;b{} ubf{ an nufPsf] :yfgaf6 u8]sf]
efu;Dd an ;g]{ b/' L an b'/L x'G5 . km] ;f] k"0f{ ¿kn] j:tl' eq u8]sf] cj:yfdf, km;] fs] f]
rf8} fO Ö tfn} b'/L / km];fs] f] nDafO Ö an b/' L xG' 5 .
km] ;fs] f] ult cg'kft (Velocity ratio of wedge)
km];f] Psflt/ km/flsnf] / df6] f] x'G5 eg] csfl]{ t/ bO' {cf6] f 58s\ ] ;tx ldn/] wfl/nf] ags] f] xG' 5
. wfl/nf] efun] rflxPsf] lbzfdf 3if0{ f lj?4 -tf}n_ sfo{ ug{ ;lhnf] agfpF5 .
km];fn] ] k0" f{ sfo{ ubf,{
ann] kf/ u/]sf] b/' L Ö km;] f]sf] ulx/fO Ö H
tf}nn] kf/ u/]sf] b/' L Ö km];f]sf] rf8} f efu -6fpsf]_ sf] df6] fO Ö L
Okmf]6{ b/' L =H lrq 8.10
ult cgk' ft (VR) Ö nf]8 b/' L L
132 lj1fg tyf kl| jlwM sIff (
pbfx/0f
;uF s} f] lrqdf km] ;fs] f] ko| fu] n] sf7 lrg{ 200 N sf] an nufOPsf] 5 . km] ;f] sf7leq l5bf{
o;sf] ;txdf 600 N a/fa/sf] 3if0{ f pTkGg xG' 5 eg] oflGqs kmfObf, ult cg'kft / sfo{
Ifdtf lx;fa ug{'xf];\ .
lbOPsf,] lrq 8.11
km] ;fd] f nufOPsf] an -E_ Ö 200 N
k]m;fs] f] ;txdf pTkGg xg' ] 3if{0f (W) = 600 N
km;] fs] f] ulx/fO -H_ Ö 10 cm
km];f]sf] rf8} f efu -6fpsf_] sf] df]6fO (L) Ö 2.5 cm
k]m;f]sf oflGqs kmfObf
W
MA =
E
600 N
= =3
200 N
Okmf]6{ b'/L
ultcg'kft (VR) Ö nf8] b/' L
Ö H = 10 = 4
L 2.5
lbOPsf] km] ;fs] f] oflGqs kmfObf 3 / ult cg'kft 4 xG' 5 .
2=-v_ kr] (Screw)
b}lgs hLjgdf k]r lsnfn] sf7sf] 6'jm| f hf]8\g], Hofs :j|ms' f] k|ofu] n] thread
ef/ p7fpg], g6af]N6n] wft'sf kftx¿ s:g] cflb u/s] f] cjnfs] g
ug{ ;lsG5 . lrq 8.12 df b]vfOP h:t} :j|md' f b'O{cf6] f 58s\ ] ;txx¿ pitch lrq 8.12
hf]l8Psf] wfl/nf] wfuf] :kfO/n -spiral_ ¿kdf al] /Psf] xG' 5 . To;}n]
kr] nfO{ :kfO/n 58s\ ] ;tx -Spiral inclined plane_ elgG5 . kr] Ps
lsnf h:t} a]ngfsf/ (Cylindrical) j:td' f 58s\ ] ;tx a]l/P/ ag]sf]
;/n oGq xf] . :j'|m klg 58\s] ;txs} ljlzi6 ¿k xf] .
lrq 8.12 df bv] fP h:t} bO' {cf]6f wfufl] arsf] efunfO{ lkr -pitch_ elgG5 . k]rnfO{ Ps kmGsf
3d' fpbF f Ps lkr a/fa/sf] b'/L j:tl' eq ;5{ . t;y{ x]8 -head_ sf] cwJ{ of; R ePsf] :j|m'
-kr] _ nfO{ Ps kmGsf] 3d' fpbF f,
lj1fg tyf k|ljlwM sIff ( 133
an b/' L Ö k]rdf 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
2πR
ult cg'kft Ö
P
k]rsf oflGqs kmfObf lkrdf e/ k5{ . lkr jf b'O{ ug' flarsf] b'/L hlt sd eof] TolQ g} sfo{
ug{ ;lhnf] x'G5 .
3. kfª\u|f / la8 (Wheel and Axle)
ljm| ofsnfk 8.4
Pp6f kfª\u|f / la“8sf] df8] n] lng'xf];\ . o;sf] kl/lwdf df]6f] wfuf] ag] x'{ f];\ . la“8df
tf}nnfO{ em'G8o\ fP/ kfª\uf| df ePsf] 8f]/Laf6 Okmf]6{ nufpgx' f];\ . nufOPsf] Okmf6] { gfKg sdfgL
t/fh' k|of]u ug{x' f];\ . km/s km/s nf]8 lngx' f;] \ / cfjZos tYofª\s ;ª\sng u//] tnsf] h:t}
tflnsfdf e/L lx;fa ug'x{ f];\ M
k|ofu] Okmf]{6 oflGqs kmfObf kfªu\ |fsf] cw{Jof; (R) la“8sf] sfo{Ifdtf
;ª\ nf8] cwJ{ of; (r) R/r
Vof
1.
2.
3.
4.
rªu\ f p8fpg n66\ fO ko| f]u x'G5 . To:t} u/L 9f]sfdf x\
ofG8n / ;fOsndf kfpbfg -paddle_ ko| fu] ul/Psf] x'G5 .
oL pks/0fx¿ kfªu\ |f / laF8sf pbfx/0fx¿ x'g\ . logLx¿n]
sfdnfO{ ;lhnf] agfp5F g\ . nfdf] cw{Jof; ePsf] a]ngf
-kfªu\ |f_ / 5f6] f] cw{Jof; ePsf] an] gf -laF8_ Pscfk;df
hf8] ]/ Pp6} cIfdf ;Fu} 3D' g ;Sg] u/L agfOPsf] ;/n lrq 8.13 kfª\u|f / la8“
oGqnfO{ kfªu\ |f / laF8 elgG5 . kfªu\ f| df an nufO{ la8F df
emG' 8\ofOPsf] tfn} nfO{ prfNbf o;df nufOPsf] an k|jw{g
(magnify) x'G5 .
kfªu\ f| / la8F sf] k|of]u u/L sfd ubf{ kfª\uf| / la8F n] cfˆgf] cIfdf Ps kmGsf] nufpFbf cfcfˆgf]
kl/lw a/fa/ 8f/] Lsf] nDafO al] /g] jf km'Sg] xG' 5 . kfªu\ |f / laF8df Okmf]6{n] kfª\uf| sf] kl/lw a/
fa/sf] b'/L kf/ ubf{ nf]8n] la8F sf] kl/lw a/fa/sf] b'/L kf/ u5{ . t;y{ kfª\u|f / la8F df,
ult cg'kft Ö Okmf6] { b/' L
nf]8 b/' L
134 lj1fg tyf k|ljlwM sIff (
Ö kfªu\ f| sf] kl/lw
laF8sf] kl/lw
olb kfªu\ |fsf] cwJ{ of; R / laF8sf] cwJ{ of; r eP,
ult cg'kft 2πR = R/r
= 2πr
t;y{ kfª\uf| / laF8df kfª\u|fsf] cwJ{ of; / laF8sf] cw{Jof;sf] A
cgk' ftn] o;sf] ult cg'kftsf] dfg lbG5 . B
kfªu\ |f / la8F nfO{ lg/Gt/ufdL pQf]ns klg elgG5 lsgeg]
o;df pQf]nsdf h:t} nf]8 / Okmf]6{ cIfsf] b'O{lt/ xG' 5 . o;sf] lrq 8.14 lg/Gt/ufdL pQf]ns
cIfdf kg{] s]Gb|nfO{ kmnjm| d -F_ sf ¿kdf lng ;lsG5 . o;n]
sfo{ ubf{ 360º 3'd/] lg/Gt/ sfo{ ub5{ . o; j|mddf lrqdf b]
vfOP h:t} kfª\u|faf6 an nufpg al] /Psf] 8f]/Ln] 5fP] sf] Okmf6] { laGb' -A_ ;+Fu;Fu+ } la8F df nf]8
em' G8\ofpg a]l/Psf] 8f/] Ln] 5f]Psf] nf8] laGb' -B_ klg kl/jt{g eO/x]sf] xG' 5 .
;fwf/0f oGqaf6 sfo{ ubf{ tfn} nfO{ 5f6] f] ;dodf cyft{ \ l56f] prfNg ;lsG5 . plt g} ;dodf
ann] kf/ ug]{ b'/LeGbf tf}nn] kf/ ug{] b'/L a9L ePdf oGqn] sfo{sf] j]u a9fp5F . pbfx/0fsf
nflu kfª\uf| / laF8 -n66\ fO_ sf] laF8af6 an nufpbF f plt g} ;dodf ann] kf/ ug]{ b/' LeGbf
tfn} n] kf/ ug{] b/' L a9L x'G5 . o; cj:yfdf sfos{ f] j]u a9\5 cyf{t\ n66\ fOdf wfuf] rf8F f]
rf8F f] a]l/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|jw{g (magnify) u5{ . pbfx/0fsf nflu rfnsn] :6l] /ª
xl\ jn -steering wheel_ df nufPsf] an k|jwg{ eO{ lgs} uxf| F} uf8Lsf] kfªu\ |fsf] lbzf kl/jtg{
xG' 5 . :6]l/ª x\ljnsf] Jof; a9b\ f an b'/L klg a9\g] ePsfn] a9L dfqfdf annfO{ kj| w{g ug{
6s« x¿sf] :6]l/ª x\ljn sf/x¿df xg' ] :6l] /ª xl\ jneGbf 7'nf] agfOPsf] x'G5 .
;/n oGqsf] ;+of]hgsf ¿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 7'nf d]
l;gsf] lrq jf >Job[Zo ;fduL| kb| zg{ ul/Psf] cjnfs] g ug'{xf];\, / lgDglnlvt kZ| gdf 5nkmn
u/L lgisifd{ f k'Ug'xf;] \ .
-s_ uf8Lsf] OlGhgnfO{ lsg hl6n oGqsf ¿kdf lnOG5 <
-v_ s] ;a} hl6n oGqx¿ ;/n oGqaf6 ags] f xG' 5g\ <
hl6n ks| [ltsf sfox{ ¿ ug{ ;fwf/0f oGqaf6 ;Dej x'bF }g, h:t}M snsf/vfgfdf h8fg ePsf
OlGhgn] hl6n ks| l[ tsf] sfo{x¿ ug{'kg]{ x'G5 . 7n' f 6s« x¿n] uxf| F} ef/ cf;] fg{] sfdx¿ ub5{ .
To:t} u/L an' 8fh] /n] af6f] vGg] sfo{ ub{5 . o;/L hl6n sfo{ ug{sf nflu ljleGg ks| f/sf
lj1fg tyf k|ljlwM sIff ( 135
;/n oGqx¿sf] ;+ofh] gaf6 hl6n oGqx¿ ag]sf x'G5g\ . h:fsf dfWodn] l56f,] ;lhnf] tyf
yf/] } an nufP/ sfo{ ug{ ;lsG5 . o;/L b'O{ jf b'Oe{ Gbf a9L ;fwf/0f oGqx¿ ldnL ag]sf
oGqnfO{ hl6n oGq elgG5 .
ljm| ofsnfk 8.6
pbfx/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
j|m=;= hl6n oGq ;/n oGq
1. jm| ]g pQf]ns / l3gL{
sfoI{ fdtf (Efficiency)
lj|mofsnfk 8.2 df lx;fa ul/Psf] l3gL{sf] ko| f]uaf6 kf| Kt xg' ] sfo{ / l3gL{df ul/Psf] sfo{sf]
cg'kftnfO{ kl| tztdf JoSt ubf{ pSt l3gL{ ko| f]u ePsf] pmhfd{ Wo] slt k|ltzt jf:tljs sfo{
ug{df vkt eof] eGg] hfgsf/L kf| Kt xG' 5 . o;;Fu} slt kl| tzt pmhf{ cGo ¿kdf ¿kfGtl/t
eof] eGg] hfgsf/L klg kf| Kt x'G5 . pbfx/0fsf nflu olb pSt cgk' ftsf] dfg 75% cfPdf
xfdLn] l3gL{ tfGbf ko| f]u u/s] f] hDdf pmhfs{ f] 75 % ;bk' of]u x'G5 / afFsL 25 % pmhf{ 3if{0fn]
ubf{ pTkGg x'g] tfk, Wjlg, cflb zlStdf ¿kfGt/0f ePsf] a'lemG5 . t;y{ xfdLn] k|ofu] u/s] f]
l3gLs{ f] sfo{Ifdtf 75 % 5 . l3gL{sf] ko| fu] af6 k|fKt x'g] sfo{ pTkflbt sfo{ xf] . pTkflbt sfo{
eGgfn] oGqdf nf]8n] ug]{ sfo{nfO{ ae' mp5F . ul0ftLo ¿kdf nV] bf,
pTkflbt sfo{ = nf8] n] ug]{ sfo{ = nf]8 x nf8] b/' L
To:t} l3gLd{ f ul/Psf] sfo{ nfut sfo{ xf] . nfut sfo{ eGgfn] oGqdf Okmf{]6n] u/s] f] sfon{ fO{
al' emG5 . ul0ftLo ¿kdf n]Vbf,
nfut sfo{ = Okmf]{6n] ug{] sfo{ = Okmf]{6 × Okmf]6{ b/' L
;/n oGqdf pTkflbt sfo{ (Output work) / nfut sfo{ (Input work) sf] cgk' ftnfO{
sfoI{ fdtf (Efficiency) elgG5 . o;nfO{ kl| tztdf JoSt ul/G5 . ul0ftLo ¿kdf
sfo{Ifdtf (Efficiency) = npTfuk ftlbtssfofo{ { × 100 %
pTkflbt sfo{ / nfut sfos{ f ;"qnfO{ sfoI{ fdtfsf] ;q" df k|lt:yfkg ubf,{
sfoI{ fdtf -η_ = nf]8 × 100 %
Okmf]6{
Okmf]6{ b'/L
nf]8 b'/L
sfo{Ifdtf -η_ = oflGqs kmfObf × 100 %
ult cgk' ft
136 lj1fg tyf k|ljlwM sIff (
;/n oGqx¿df pTkflbg sfo{ hlxn] klg nfut sfoe{ Gbf sd x'G5 . sfo{Ifdtf ztk|ltzt
x'gsf nflu ;Dk"0f{ nfut sfo{ pTkflbt sfo{df kl/0ft ePsf] xg' 'k5{ . ;/n oGqx¿df xg' ]
3if0{ fsf sf/0fn] ubf{ ;Dk"0f{ nfut sfo{ pTkflbt sfo{df kl/0ft x'g ;Sb}g . h;n] ubf{ ;/n
oGqsf] sfoI{ fdtf hlxn] klg ztk|ltzteGbf sd x'G5 . ;/n oGqdf t]n jf luh| sf] ko| fu] n]
3if{0f 36fP/ o;sf] sfo{ Ifdtf s]xL a9fpg ;lsG5 .
k0" f{ oGq (Perfect machine)
nfut sfo{ / pTkflbt sfo{ a/fa/ ePsf] cj:yfdf sfoI{ fdtf ztk|ltzt xG' 5 . o:tf]
sfNklgs cj:yfsf] oGqnfO{ k0" f{ oGq (perfect machine) elgG5 . k0" f{ oGqdf oflGqs kmfObf /
ult cgk' ft klg a/fa/ xG' 5 . o; lsl;dsf] oGqdf nfut sfo{df s'g} x|f; cfpbF g} . Jojxf/
df 3if0{ f/lxt oGq ;Dej x'bF g} . t;y{ k0" f{ oGq Jojxf/df ;Dej 5g} .
pbfx/0f
sg' } l3gL{ k|0ffnLsf] sfoI{ fdtf 80% 5 / oflGqs kmfObf 4 x'gsf nflu pSt k|0ffnLsf] l3gL{
;ª\Vof slt xg' k5{ < To; l3gL{ k0| ffnLdf 1000N sf] nf8] p7fpg slt Okmf6{] rflxPnf <
oxfF,
sfo{Ifdtf -η_ Ö 80%
oflGqs kmfObf (MA) = 4
nf]8 (L) = 1000N
l3gL{ ;ª\Vof = ?
Okm]f{6 (E) = ?
;q" cg';f/,
sfo{Ifdtf -η_ = MA × 100 %
× 100 %
VR =5
or 80% = 4
VR
or VR = 400
80
To;}n] l3gL{ ;ªV\ of = 5
km/] L MA L or 4 = 1000 or E = 1000
= E
E4
To;n} ] Okmf{6] = 250 N
lj1fg tyf kl| jlwM sIff ( 137
cEof;
!= tn lbOPsf kZ| gsf] ;xL pQ/df l7s lrx\g -√_ nufpg'xf];\ M
-s_ Ps rSs] crn l3gL{af6 oflGqs kmfObf geP klg o;sf] ko| fu] lsg ul/G5 <
-c_ ansf] dfqf a9fpg -cf_ j:ts' f] ult a9fpg
-O_ sfo{ Ifdtf a9fpg -O{_ ansf] lbzf kl/jt{g ug{
-v_ tLg kfª\u|] rn l3gL{sf] ult cg'kft slt x'G5 <
-c_ Ps -cf_ bO' { -O_ tLg -O_{ rf/
-u_ @ ld6/ cUnf] 6«sdf ;fdfg r9fpg 6m nfdf] kmns] ko| fu] u/L 58s\ ] ;txsf]
lgdf0{ f ul/Psf] 5 eg] pSt 58s] ;txsf] ult cg'kft slt xfn] f <
-c_ Ps -cf_ bO' { -O_ tLg -O{_ rf/
-3_ k0" f{oGqsf] sfo{Ifdtf slt xG' 5 <
-c_ 100% -cf_ <100% -O_ >100% -O{_ 0%
-ª_ Ps kfªu\ |] 7n] fuf8f s'g s'g ;/n oGq ldnL ags] f] x'G5 <
-c_ kfª\uf| / la8F tyf pQfn] s -cf_ l3gL{ / km];f]
-O_ 58s\ ] ;tx / k]r -O_{ pQf]ns / km];f]
@= km/s nV] gx' f;] \ M
-s_ l3gL{ / kfªu\ |f tyf laF8
-v_ VR / MA
-u_ Jack Screw / aGr/f]
-3_ pTkflbt sfo{ / nfut sfo{
#= sf/0f lbg'xf];\ M
-s_ kxf8df r9g\ 3'dfp/f] af6f] agfPsf] x'G5 .
-v_ jm| ]gnfO{ hl6n oGq elgG5 .
-u_ sg' } klg oGqsf] sfoI{ fdtf ztk|ltzt x'Fb}g .
-3_ jf:tljs oGqsf] oflGqs kmfObf ult cgk' fteGbf sd x'G5 .
-ª_ kfª\uf| / laF8nfO{ lg/Gt/ufdL pQfn] s elgG5 .
138 lj1fg tyf kl| jlwM sIff (
$= k|Zgsf] pQ/ n]Vg'xf;] \ M
-s_ ;/n oGq egs] f] s] xf] < o;sf kmfObf n]Vgx' f];\ .
-v_ hl6n oGq eg]sf] s] xf] < pbfx/0f;lxt JofVof ugx{' f];\ .
-u_ 58\s] ;txnfO{ pbfx/0f;lxt k:| 6 kfg'{xf;] \ .
-3_ km];f] egs] f] s] xf] < pbfx/0f;lxt o;sf] dxŒj nV] g'xf];\ .
-ª_ k]r sn] fO{ elgG5 < bl} gs hLjgdf k]rsf] k|ofu] s] s] sfdsf nflu ul/G5 <
-r_ l3gL{sf ks| f/nfO{ lrq;lxt kl/ro lbg'xf;] \ .
-5_ kr] / km;] f]sf oflGqs kmfObf / ultcg'kft s;/L lgsflnG5 < lrq;lxt JofVof
ug{'xf];\ .
-h_ 58\s] ;txsf oflGqs kmfObf / ult cg'kft s;/L a9fpg ;lsG5 < pbfx/0f;lxt
n]Vgx' f];\ .
-em_ sg' } oGqsf] sfo{Ifdtf 75% eGgfn] s] al' emG5 <
-`_ b}lgs hLjgdf k0" f{ oGq c;Dej h:t} xG' 5 < sf/0f;lxt JofVof ugx'{ f;] \ .
-6_ kfªu\ |f / laF8sf] ult cgk' ft s;/L kQf nufOG5, lrq;lxt k|:6 kfgx'{ f];\ .
-7_ lgDglnlvt hl6n oGq sg' sg' ks| f/sf ;/n oGq ldnL ag]sf] xG' 5, nV] g'xf];\ M
-c_ nu' f l;pg] d]l;g -cf_ l:6r d]l;g
-O_ ;fOsn -O_{ lk7f] lk:g] d]l;g
%= ul0ftLo lx;fax¿ ugx'{ f];\ M
-s_ lrqdf b]vfOPsf] 58s\ ] ;txsf 300N 5m
nflu oflGqs kmfObf, ult cg'kft / 20 m
sfo{Ifdtf lx;fa ug'{xf;] \ . 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 p7fpbF f x'g] nfut sfo{ / pTkflbt
sfo{ lx;fa ug{'xf;] \ .
-Effort = 312.5 N , MA = 3.2, nfut sfo{ Ö 7500 J, pTkflbt sfo{ Ö 6000 J_
lj1fg tyf k|ljlwM sIff ( 139
-u_ kfª\u|f / laF8sf] 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_ ;Fu+ }sf] lrqdf km;] fs] f] ko| f]un] sf7sf d'9f 6 cm
lrb}{ u/]sf] b]vfOPsf] 5 . pSt km] ;fs] f] rf8} fO
6 cm / ulx/fO 12 cm 5 . km];f]df 300 N km;] f]
an nufpFbf 500 N a/fa/sf] cj/fW] f -tfn} _
pTkGg x'G5 eg] o;sf oflGqs kmfobf, ult 12 cm
cgk' ft / sfo{Ifdtf lx;fa ug'{xf];\ .
-Ans: MA = 1.67, VR = 2, η=83.33 %_ sf7sf] d9' f
140 lj1fg tyf kl| jlwM sIff (
( phf{
(Energy)
lrq 9.1: tfkn] kfgL afkmdf kl/jtg{ xb“' } lrq 9.2: laB't\af6 rNg] :s6' /
lrq 9.3: vfgf ksfpg Uof;“ sf] ko| fu] lrq 9.4: pmhfs{ f] ¿kfGt/0f
-c_ lrq 9.1 df sg' phfn{ ] n'uf ;'ss] f] b]vfOPsf] 5 <
-cf_ On]lS6«s :s6' /n] s'g phf{ ko| fu] u5{ <
-O_ vfgf ksfpg s'g s'g phf{sf] ;f| t] k|ofu] ul/G5 <
-O_{ ;o' a{ f6 k|fKt x'g] phfn{ fO{ sg' s'g :j¿kdf ¿kfGt/0f ug{ ;lsG5 <
;o" { phf{sf] k|d'v ;f| t] xf] . ;o' {lagf hLjg ;Dej xb'F }g . hnrj|m ;~rfng ug,{ la?jfn] vfgf
agfpg, la:sg' ;s' fpg, bfp/f ;'sfpg cflb s}og sfo{x¿df ;"oa{ f6 kf| Kt xg' ] phf{sf] kT| oIf
pkofu] xG' 5 . vfgLx¿df kfOg] k]6f« l] nod kbfy,{ k|fs[lts UofF; nufot hnljB't\ cflb klg
ckT| oIf ¿kdf ;fo} { phf{sf ¿kflGtl/t cj:yf x'g\ . To;n} ] phfs{ f k|foM ;a} ;f| t] x¿ ;f}o{
phfa{ f6 k|ToIf jf ckT| oIf ¿kfGt/0f eO{ ags] f xG' 5g\ .
lj1fg tyf k|ljlwM sIff ( 141
pmhfs{ f ;|f]t (Source of energy)
lj|mofsnfk 9.1
tnsf lrqdf xfd|f] b]zsf ljleGg If]qdf dflg;n] ko| fu] ug]{ pmhfs{ f ;f| t] x¿ bv] fOPsf 5g\ .
lrqx¿sf] cWoog u/L 5nkmn ug'{xf];\ .
u'OF7f bfp/f PnkL Uof;F
ufa] / Uof;F k]6«fl] nod tn] laj|m6]
-c_ lrqdf phfs{ f sg' s'g ;|f]tx¿ b]vfOPsf 5gl\r<q 9.5
-cf_ oL pmhf{sf ;|f]tx¿ s;/L k|fKt xG' 5g\ <
-O_ tL ;|f]tx¿dWo] s'g sg' ;f| t] x¿ ks| [ltdf lg/Gt/ kfOG5g\ <
-O_{ sg' sg' ;f| t] x¿ ks| l[ tdf lg/Gt/ pTkfbg xg' g;sL lglZrt ;dokl5 ;dfKt xG' 5g\ xfn] f <
xfdL ljleGg ;f| ]tx¿af6 cfjZos pmhf{ k"lt{ ul//x]sf x'G5fF} . ko| f]uofU] o pmhf{ lgsfNg ;lsg]
sg' } klg j:t' pmhfs{ f] ;f| ]t xf] . sfO] nf, k]6«f]n, l8h]n, dl6t]n, kf| sl[ ts UofF;, hnljBt' cflb
pmhf{sf ;f| ]tx¿ x'g\ . gk] fnsf ljleGg If]qx¿df lahn' L, k]6f« l] nod kbfy{, bfp/f, u'OF7f, afof]
Uof;F , ;fo} { pmhf{, cflbaf6 pmhfs{ f] cfkl" t{ xG' 5 . pmhf{sf ;f| t] nfO{ dV' o b'O{ k|sf/df juL{s/0f
ug{ ;lsG5 h'g lgdgfg;' f/ 5g\ M
cgjLs/0fLo pmhf{sf] ;|ft] -Nonrenewable source of energy _
ks| [ltdf sx] L pmhf{ ;|f]tx¿ nfvf}F jifs{ f] ;dokZrft\ tof/ xG' 5g\ . To:tf ;|f]tx¿sf] e08f/
l/lQbf 5f6] f] cjlwdf pTkfbg ug{ ;lsbF }g . ltgnfO{ sfnfGt/;Dd lg/Gt/ ko| fu] u/L pmhf{ k|fKt
ug{ ;lsFbg} . ko| f]u ub{} hfFbf l/lQg] jf cfjZos k/]sf] jn] f kg' M pTkfbg ug{ g;lsg] phf{sf
;f| t] x¿nfO{ cgjLs/0fLo phfs{ f ;f| t] elgG5, h:t}M sf]Onf, vlgh t]n, kf| s[lts Uof;F cflb .
gjLs/0fLo pmhfs{ f] ;f| ]t -Renewable source of energy _
sx] L pmhf{sf ;f| t] x¿ 5f]6f] cjlwdf k'gM kl" t{ ug{ ;lsG5 . ltgnfO{ ko| fu] ub{} hfbF f ;bfsf nflu
l/lQbg} g\ . cyft{ \ cfjZos k/]sf] jn] f ltgnfO{ lgdf{0f ug{ ;lsG5 . ks| [ltdf lg/Gt/ ¿kdf
142 lj1fg tyf k|ljlw M sIff (
pTkfbg eO/xs] f / ck'u gxg' ] ;|f]tx¿ pmhf{sf gjLs/0fLo ;|f]t xg' \, h:t}M ;f}o{ phf,{ jfo'
phf{, hnljB't, bfp/f, u'O7F f, ufa] /Uof;F cflb .
;f}o{ pmhf{ -Solar energy_
k|ToIf ¿kdf ;o" a{ f6 k[YjLn] k|fKt ug]{ k|sfz / tfk ;f}o{ pmhf{ xf] . ckT| oIf ¿kdf ljleGg
k|ljlwx¿af6 klg ;fo} { pmhf{ k|ofu] ug{ ;lsG5, h:t} M ;o" s{ f] tfk / ks| fznfO{ ljBt' d\ f
¿kfGt/0f u/]/ . ;fo} { pmhf{ kY[ jLdf pmhfs{ f] dV' o ;|ft] xf] . ;f}o{ pmhf{sf sf/0f k[YjLdf hLjg
;Dej 5 . kY[ jLn] x/]s lbg k|ToIf ¿kdf ;"oa{ f6 7'nf] dfqfdf pmhf{ k|fKt u5{ . ;o" d{ f ePsf
xfO8f« h] gsf k/df0f'x¿ ;+of]hg eP/ olt 7n' f] dfqfdf pmhf{ pTkGg xG' 5 .
;"o{;“u ;DalGwt s]xL tYofª\sx¿
;o" s{ f] lk08 = 2×1030 kg, kY[ jLaf6 ;o" s{ f] b'/L = 1.5×108 km, ;"o{sf] sf/] sf] tfkj|md sl/a
= 15,000,000 K, ;"o{sf] ;txsf] tfkj|md = 5778 K, ;o" a{ f6 pTkGg xg' ] zlSt = 3.8×1026 J/s
, ;f}o{ ljls/0fsf ¿kdf k[YjLsf] kl| t ju{ld6/ Ifq] kmndf cfOkU' g] pmhf{ = 1.4 kW
;o" {df x'g] Gol' Sno/ k|ltlj|mof -Nuclear reaction in the sun _
hfgsf/Lsf nflu
s]xL tŒjsf km/s km/s k/df0f'x¿ xG' 5g\ . kf/df0flds ;ªV\ of Pp6} x'g] t/ kf/df0fljs
lk08 km/s km/s xg' ] k/df0f'x¿ cfO;f6] fk] x'g\ . pbfx/0fsf nflu kf| l] 6od, 8o\ 6' ]l/od,
/ l6l« 6od xfO8f« ]hgsf cfO;f]6f]k x'g\ .
;"o{ Ps kz| :t dfqfdf xfO8«fh] g UofF; /xs] f] dWod cfsf/sf] tf/f xf] . ;o" {sf] sf/] nueu 15
ldlnog oC sf] pRr tfkjm| d 5 . olt pRr tfkjm| ddf xfO8«fh] g k/df0fx' ¿sf] On]S6f« g] x¿ k/
df0fa' f6 cnu xFb' f xfO8f« ]hg cfog -H+_ aG5g\ . o;sf ;fy} sf/] df xfO8f« h] g cfogx¿ cyf{t\
k|f]6fg] x¿ lar pRr ljsif0{ f x'g] eP tfklg pRr rfkn] ltgLx¿nfO{ ;+ofh] gsf nflu glhs
Nofp5F . ;"o{ h:t} tf/fx¿df pRr tfkj|md / rfksf] pkl:yltdf xfO8f« ]hg k/df0f'x¿ ;+of]hg
eO{ lxlnod k/df0fx' ¿ aGg] k|lj|mofnfO{ ydfG{] o'lSno/ ˆo'hg elgG5 . o; kl| j|mofdf ljls/0fsf
¿kdf 7'nf] dfqfdf pmhf{ lg:sG5 . o; k|lj|mofnfO{ tn bv] fOP h:t} tLg r/0fx¿df kb| zg{
ug{ ;lsG5 M
-c_ bO' {cf]6f kf| 6] fg] x¿ ;o+ fh] g eO{ xfO8«fh] g cfO;f]6fk] 8o\ '6]l/od -1H2_ ;uF } kfl] h6«f]g (1eo)
aG5 .
1H1 +1H1 1H2 + 1e0 + energy
-cf_ dflyNnf] r/0fdf aGg] 8o\ '6l] /od;Fu csf]{ kf| ]6fg] ;o+ fh] g eO{ xns' f] lxlnod cfO;f6] fk] - He3_
2
aG5 .
1H2 + 1H1 2He3 + γ- radiation
lj1fg tyf kl| jlwM sIff ( 143
-O_ cGtdf bO' c{ f]6f lxlnod cfO;f6] f]k ldn/] xfO8«fh] g af6 lxlnod aGg] kl| jm| of k/" f xG' 5 .
o; r/0fdf b'Oc{ f]6f kf| 6] fg] klg pTkGg x'G5g\ .
2He3 + 2He3 2He4 + 1H1 + 1H1 + energy
;du| ydfG{] ol' Sno/ ˆoh' g kl| tljm| ofnfO{ tn pNnv] ul/P emF} 5f6] s/Ldf klg nV] g ;lsG5 .
4 1H1 2He4 + 2 1e0 + energy
o;/L ;o" d{ f ljleGg r/0fx¿ kf/ u/]/ rf/cf6] f H k/df0fx' ¿sf] ;+ofh] gaf6 Pp6f He
k/df0f' aG5 . of] kl| jm| ofdf kz| :t pmhf{ pTkfbg x'G5 .
;o" {df ydfG{] o'lSno/ km\ o'hgsf] nflu pkoS' t cj:yfx¿
-c_ k|r/' dfqfdf xfO8f« h] g M ;o" {df kofK{ t dfqfdf xfO8«f]hg x'G5 h;n] ydf]G{ o'lSno/ ˆo'hgnfO{
hf/L /fV5 .
-cf_ pRr tfkj|md M ;"os{ f] pRr tfkj|mdn] :jtGq ¿kdf /xs] f kf| 6] f]gx¿ agfpF5 .
O_ pRr rfk M ;"o{sf] sf]/df kg]{ pRr rfkn] k|f6] fg] x¿nfO{ ;+of]hgsf nflu glhs Nofp5F .
hfgsf/Lsf nflu
cfOG;6fOgsf] lk08 pmhf{ ;DaGw -Einsteins’ mass-energy relation_, E = mc2 (hxfF ’m’
n] Go'lSno/ k|ltlj|mofdf gfz x'g] lk08nfO{ hgfpF5 / ’c’ n] k|sfzsf] ju] nfO{ hgfp5F _
sf cfwf/df Go'lSno/ kl| tljm| ofaf6 pTkGg xg' ] pmhf{ lx;fa ug{ ;lsG5 . pbfx/0fsf
nflu olb s'g} Gol' Sno/ k|ltlqmofdf 0.1 g lk08 gfz ePdf To;af6 lg:sg] pmhf{
lgDgfg';f/ lx;fa ug{ ;lsG5 M
E = mc2 = 10-4 × ( 3 × 108 )2 = 9× 1016 ×10-4 = 9 × 1012 J
Go'lSno/ k|ltlj|mofdf Psbd} ;fgf] lk08 gfz xb'F f klg 7'nf] kl/df0fdf pmhf{ lg:sG5 .
pmhfs{ f] kd| v' ;f| ]tsf ¿kdf ;o" { -Nonrenewable source of energy _
ljm| ofsnfk 9.2
tn lbOPsf] lrqsf] cWoog ugx'{ f];\ . lrqdf bv] fOPsf] af0f lrGgnfO{ k5\ofpb“ } ;f}o{ pmhf{df
cfwfl/t ljleGg pmhf{sf ;f| t] x¿ 7Dofpg'xf];\ / ab'“ fut ¿kdf l6Kgx' f];\ . pSt ;f| t] ;fo} { pmhf{sf]
pkh s;/L eof,] ;d"xdf 5nkmn ugx{' f];\ .
144 lj1fg tyf kl| jlw M sIff (
lrq 9.6 pmhfs{ f] kd| v' ;f| t] sf ¿kdf ;o" {
kY[ jLdf pknAw ;Dk"0f{ zlStsf ;|f]tx¿ h:tM} hnljBt' , jfo' phf{, h}ljs phf{, hLjfjz]if phf{
cflb ;a} ;fo} { pmhf{ ¿kfGt/0f eP/ ag]sf x'g\ . To;n} ] ;o" {nfO{ zlStsf] d"n ;f| ]t dflgG5 .
o;;DaGwL s]xL pbfx/0fx¿ tn pNn]v ul/Psf 5g\ .
hn;|f]t phf{ -Water energy_
hn rj|mnfO{ xfO8«fn] fl] hsn ;fOsn -Hydrological cycle_ klg elgG5 . of] rjm| df ;"o{sf] tfkn]
lxpF / a/kmsf l9Ssfx¿ kUnG5 / kfgLsf ;|f]tx¿df kfgL el/G5 . tfn, gbL, vfn] f, hnfzo
/ ;d'›sf] kfgL tfTbf afkmdf kl/0ft xG' 5 . hnjfik jfo'd08ndf lrl:;P/ afbn aG5 / jiff{
x'G5 . jiffs{ f] kfgL gbLdf axG5 jf hnfzodf hDdf xG' 5 . pSt kfgLnfO{ 7'nf afwF df hDdf
u/L lah'nL pTkfbg ul/G5 . o;/L hnljBt' ckT| oIf ¿kdf ;f}o{ pmhfa{ f6 kf| Kt x'G5 .
hLjfz]if phf{ -Fossil fuel_
kY[ jLdf k'Ug] ;"os{ f] pmhfs{ f] Ps ;fgf] c+z ks| fz ;Z+ ni] f0f kl| j|mofdfkmt{ xl/of] la?jfx¿n]
cjzf]lift ub5{ . o; k|ljm| ofdf, sfag{ 8fOcS;fO8 / kfgL :6fr{df kl/0ft x'G5 . To;kl5
;"os{ f] pmhf{ /f;folgs pmhf{df kl/0ft eO{ la?jfsf ljleGg efux¿df e08f/0f x'G5 . o;/L
e08f/ ePsf] kbfy{nfO{ hgfj/x¿n] vfgfsf ¿kdf pkefu] u5{g\ . t;y{ ck|ToIf ¿kdf
xfdLn] vfgfaf6 kf| Kt ug]{ pmhf{ klg ;"oa{ f6 kf| Kt xG' 5 . hLjfz]if OGwg sf]Onf, k]6«f]n, l8h]n,
k|fsl[ ts Uof;F cflb klg kY[ jLsf] ;txleq nfvfF} jif;{ Dd k'l/Psf d[t la?jf tyf hgfj/af6
aG5g\ . o;/L hLjfjz]if phf{ ;fo} { zlStsf] pkh xf] . sf7, jg:klt, afnLsf cjz]if, kmfx] f]/ cflb
hl} js kbfyx{ ¿ klg pmhf{sf ;f| ]tsf ¿kdf k|of]u ul/G5g\ . logLx¿ klg ;f}o{ pmhfs{ f pkh
x'g\ .
lj1fg tyf kl| jlwM sIff ( 145
jfo' phf{ -Wind energy_
jfo' pmhf{ klg ;fo} { pmhfd{ f cfwfl/t 5 . ;o" s{ f] tfkn] hldgsf] ;tx glhs /xs] f] xfjf tfT5 . pSt
tftf] xfjf xn'sf xG' 5 / dfly hfG5 . To; 7fFpdf cGoq af6 lr;f] xfjf cfpF5 . o; jm| ddf
axg] xfjfaf6 jfo' phf{ pTkfbg ug{ ;lsG5 . o;/L jfo' phf{ klg ;fo} { phfs{ } pkh xf] .
;fo} { pmhf{ kf| Kt ug{] kl| jlw -Solar energy harvesting technology)
;fn] f/ Kofgn ;fn] f/ 6s' L ;fn] f/ l:66« aQL
;fn] f/ 8f« o/ ;fn] f/ jf6/ lx6/ ;fn] f/ ss' /
lrq 9.7
kl| jlwsf] ko| f]un] ;fo} { pmhfn{ fO{ cGo pmhfd{ f kl/jt{g ul/G5 . pbfx/0fsf nflu ;fn] f/ Kofgnsf
dfWoodaf6 ;f}o{ pmhf{nfO{ ljBt' \df kl/jtg{ ug{ ;lsG5 . s]xL dflg;n] 3/sf] 5fgfdf ;"o{sf]
tfkaf6 kfgL ttfpg] ;f]nf/ jf6/ lx6/ -Solar water heater_ /fv]/ kfgL tftf] kfg]{ u5g{ \ . of]
Ps ;f}o{ pmhf{ k|fKt ug]{ kl| jlwsf] pbfx/0f xf] . To:t} bl} gs hLjgdf ko| fu] x'g] ;fn] f/ 6'sL
-Solar lamp_, ;f]nf/ l:6«6 aQL -Solar street lamp_, ;fn] f/ 8f« o/ -Solar dryer_, ;fn] f/ 8«fo/
-Solar cooker_ cflb ;fo} { pmhf{ k|fKt ug{] kl| jlwx¿ xg' \ .
;f}o{ ljBt' \ -Solar Electricity_
;f]nf/ Kofgnsf] k|ofu] af6 ;fo} { pmhfn{ fO{ ljBt' d\ f
¿kfGt/0f u/L ljleGg lsl;dsf ljBt' \ pks/0fx¿
rnfpg ;lsG5 . of] yk' }| kmf6] f]efN] 6o] s ;n]
-Photovoltaic cell_ x¿sf] ;d"x xf] . oL ;]nx¿ lrq 9.8 kmf6] fe] fN] 6o] s ;n]
cw{;r" fns -Semiconductor_ kbfy{, ;fdfGotof
l;lnsg -Silicon_ af6 ags] f x'G5g\ . logdf
;"oa{ f6 cfPsf] k|sfz kbf{ l;lnsn k/df0fx' ¿af6
OnS] 6f« ]g :jtGq aGb} rNg yfN5g\ / ;n] sf b'O{ 5]plar ljBt' \ wf/f pTkGg xG' 5 . ;;fgf ;]nx¿nfO{
>]0fLqmd h8fg ubf{ ljB't\wf/fsf] dfqf a95\ . k|sfzsf] tLjt| f hlt a9L xG' 5, ljBt' sf] kj| fx
Tolt g} a9L x'G5 . To;sf/0f ;f]nf/ Kofgnaf6 k"0f{ Ifdftfdf ljBt' \ k|fKt ug{ o;nfO{ /fd/| L 3fd
kg{] :yfg 5gf6] u/L /fVgk' 5{ .
146 lj1fg tyf kl| jlw M sIff (
The words you are searching are inside this book. To get more targeted content, please make full-text search by clicking here.
Science_Class-9_2079
Discover the best professional documents and content resources in AnyFlip Document Base.
Search