enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion sin cos 4. Point Mss. () n object cn be considered s point object if durin otion in iven tie, it covers distnce uch reter thn its own size. () Object with zero diension considered s point ss. () Point ss is theticl concept to siplify the probles. 4. Inerti. () Inherent property of ll the bodies by virtue of which they cnnot chne their stte of rest or unifor otion lon striht line by their own is clled inerti. () Inerti is not physicl quntity, it is only property of the body which depends on ss of the body. () Inerti hs no units nd no diensions (4) wo bodies of equl ss, one in otion nd nother is t rest, possess se inerti becuse it is fctor of ss only nd does not depend upon the velocity. 4. Liner Moentu. () Liner oentu of body is the quntity of otion contined in the body. () It is esured in ters of the force required to stop the body in unit tie. () It is esured s the product of the ss of the body nd its velocity i.e., Moentu = ss velocity. If body of ss is ovin with velocity v then its liner oentu p is iven by p v (4) It is vector quntity nd it s direction is the se s the direction of velocity of the body. (5) Units : k-/sec [S.I.], -c/sec [C.G.S.] (6) Diension : [ ML ] (7) If two objects of different sses hve se oentu, the lihter body possesses reter velocity. p v v v v i.e. = constnt v [s p is constnt] (8) or iven body p v (9) or different bodies t se velocities p v p = constnt p = p v = constnt v
Newton s Lws of Motion 4.4 Newton s irst Lw. body continue to be in its stte of rest or of unifor otion lon striht line, unless it is cted upon by soe externl force to chne the stte. () If no net force cts on body, then the velocity of the body cnnot chne i.e. the body cnnot ccelerte. () Newton s first lw defines inerti nd is rihtly clled the lw of inerti. Inerti re of three types : Inerti of rest, Inerti of otion, Inerti of direction () Inerti of rest : It is the inbility of body to chne by itself, its stte of rest. his ens body t rest reins t rest nd cnnot strt ovin by its own. Exple : (i) person who is stndin freely in bus, thrown bckwrd, when bus strts suddenly. When bus suddenly strts, the force responsible for brinin bus in otion is lso trnsitted to lower prt of body, so this prt of the body coes in otion lon with the bus. While the upper hlf of body (sy bove the wist) receives no force to overcoe inerti of rest nd so it stys in its oriinl position. hus there is reltive displceent between the two prts of the body nd it ppers s if the upper prt of the body hs been thrown bckwrd. Note : If the otion of the bus is slow, the inerti of otion will be trnsitted to the body of the person uniforly nd so the entire body of the person will coe in otion with the bus nd the person will not experience ny jerk. (ii) When horse strts suddenly, the rider tends to fll bckwrd on ccount of inerti of rest of upper prt of the body s explined bove. (iii) bullet fired on window pne kes clen hole throuh it while stone breks the whole window becuse the bullet hs speed uch reter thn the stone. So its tie of contct with lss is sll. So in cse of bullet the otion is trnsitted only to sll portion of the lss in tht sll tie. Hence cler hole is creted in the lss window, while in cse of bll, the tie nd the re of contct is lre. Durin this tie the otion is trnsitted to the entire window, thus cretin the crcks in the entire window. (iv) In the rrneent shown in the fiure : Crcks by the bll () If the strin is pulled with sudden jerk then it will experience tension while due to inerti of rest of ss M this force will not be trnsitted to the strin nd so the strin will brek. (b) If the strin is pulled stedily the force pplied to it will be trnsitted fro strin to throuh the ss M nd s tension in will be reter thn in by M (weiht of ss M) the strin will brek. (v) If we plce coin on sooth piece of crd bord coverin lss nd strike the crd bord piece suddenly with finer. he crdbord slips wy nd the coin flls into the lss due to inerti of rest. Hole by the bullet (vi) he dust prticles in durree flls off when it is beten with stick. his is becuse the betin sets the durree in otion wheres the dust prticles tend to rein t rest nd hence seprte. (4) Inerti of otion : It is the inbility of body to chne itself its stte of unifor otion i.e., body in unifor otion cn neither ccelerte nor retrd by its own. Exple : (i) When bus or trin stops suddenly, pssener sittin inside tends to fll forwrd. his is becuse the lower prt of his body coes to rest with the bus or trin but the upper prt tends to continue its otion due to inerti of otion. M
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion (ii) person jupin out of ovin trin y fll forwrd. (iii) n thlete runs certin distnce before tkin lon jup. his is becuse velocity cquired by runnin is dded to velocity of the thlete t the tie of jup. Hence he cn jup over loner distnce. (5) Inerti of direction : It is the inbility of body to chne by itself direction of otion. Exple : (i) When stone tied to one end of strin is whirled nd the strin breks suddenly, the stone flies off lon the tnent to the circle. his is becuse the pull in the strin ws forcin the stone to ove in circle. s soon s the strin breks, the pull vnishes. he stone in bid to ove lon the striht line flies off tnentilly. (ii) he rottin wheel of ny vehicle throw out ud, if ny, tnentilly, due to directionl inerti. (iii) When cr oes round curve suddenly, the person sittin inside is thrown outwrds. Proble. Solution : () Proble. Solution : (d) Sple proble bsed on Newton s first lw When bus suddenly tkes turn, the psseners re thrown outwrds becuse of () Inerti of otion (c) Speed of otion [MC 999; CPM 000, 00] (b) ccelertion of otion (d) oth (b) nd (c) person sittin in n open cr ovin t constnt velocity throws bll verticlly up into ir. he bll fll () Outside the cr (c) In the cr to the side of the person [EMCE (Med.) 995] (b) In the cr hed of the person (d) Exctly in the hnd which threw it up ecuse the horizontl coponent of velocity re se for both cr nd bll so they cover equl horizontl distnces in iven tie intervl. 4.5 Newton s Second Lw. () he rte of chne of liner oentu of body is directly proportionl to the externl force pplied on the body nd this chne tkes plce lwys in the direction of the pplied force. () If body of ss, oves with velocity v then its liner oentu cn be iven by p v nd if force is pplied on body, then dp dp K dt dt dp or (K = in C.G.S. nd S.I. units) dt d dv dv or ( v) (s ccelertion produced in the body) dt dt dt Proble. Solution : () orce = ss ccelertion Sple proble bsed on Newton s second lw trin is ovin with velocity 0 /sec. on this, dust is fllin t the rte of 50 k/in. he extr force required to ove this trin with constnt velocity will be [PE 999] () 6.66 N (b) 000 N (c) 66.6 N (d) 00 N orce d 50 v 0 6.66 N dt 60 Proble 4. force of 0 Newton cts on body of ss 0 k for 0 seconds. Chne in its oentu is[mp PE 00]
4 4 Newton s Lws of Motion () 5 k /s (b) 00 k /s (c) 00 k /s (d) 000 k /s u = 0 v = 0 u = 0 v > 0 ody reins t rest. Here force is tryin to chne the stte of rest. ody strts ovin. Here force chnes the stte of rest. Solu tion : (b) Pro ble 5. u 0 v > u In sll intervl of tie, force increses the nitude of speed nd direction of otion reins se. () Solu tion : () u v < u In sll intervl of tie, force decreses the nitude of speed nd direction of otion reins se. d orce dt v = v v ) orce is n externl effect in the for of push or pulls which (i) Produces or tries to produce otion in body t rest. (ii) Stops or tries to stop ovin body. In unifor circulr otion only direction of velocity chnes, speed reins constnt. orce is lwys perpendiculr to velocity. In non-unifor circulr otion, ellipticl, prbolic or hyperbolic otion force cts t n nle to the direction of otion. In ll these otions. oth nitude nd direction of velocity chnes. (iii) Chnes or tries to chne the direction of otion of the body. 00(0 5 0. 5000N 4.6 or ce. ( () Diension : orce = ss ccelertion [ ] [ M][ L ] [ ML ] () Units : bsolute units : (i) Newton (S.I.) (ii) Dyne (C.G.S) Grvittionl units : (i) Kilor-force (M.K.S.) (ii) Gr-force (C.G.S) Newton : Dyne : One Newton is tht force which produces n ccelertion of ss Kilor. Newton k / s One dyne is tht force which produces n ccelertion of r. Dyne c / sec eltion between bsolute units of force Newton Kilor-force : It is tht force which produces n ccelertion of k-f = 9.8 Newton Gr-force : It is tht force which produces n ccelertion of. -f = 980 Dyne eltion between rvittionl units of force : k-f = 5 0 Dyne 7 0 -f / s in body of c / s in body of ss 9.8 / s in body of ss k. 980 c / s in body of ss
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 5 (4) forul is vlid only if force is chnin the stte of rest or otion nd the ss of the body is constnt nd finite. d dv d (5) If is not constnt ( v) v dt dt dt (6) If force nd ccelertion hve three coponent lon x, y nd z xis, then ˆi ˆj kˆ nd ˆi ˆj kˆ x y z x y z ro bove it is cler tht x,, x y y z z (7) No force is required to ove body uniforly lon striht line. 0 (s 0 ) (8) When force is written without direction then positive force ens repulsive while netive force ens ttrctive. Exple : Positive force orce between two siilr chres Netive force orce between two opposite chres (9) Out of so ny nturl forces, for distnce force wekest. nucler electro netic rvittionl (0) tio of electric force nd rvittionl force between two electron 5 0 etre, nucler force is stronest while rvittionl 4 e / 0 e () Constnt force : If the direction nd nitude of force is constnt. It is sid to be constnt force. () Vrible or dependent force : (i) ie dependent force : In cse of ipulse or otion of chred prticle in n lterntin electric field force is tie dependent. (ii) Position dependent force : Grvittionl force between two bodies qq or orce between two chred prticles. 4 r (iii) Velocity dependent force : Viscous force ( 6 rv) orce on chred prticle in netic field ( qv sin ) () Centrl force : If position dependent force is lwys directed towrds or wy fro fixed point it is sid to be centrl otherwise non-centrl. G 0 r Exple : Motion of erth round the sun. Motion of electron in n to. Sctterin of -prticles fro nucleus. Sun Erth + Nucleus Electron + Nucleus + - (4) Conservtive or non conservtive force : If under the ction of force the work done in round trip is zero or the work is pth independent, the force is sid to be conservtive otherwise non conservtive.
6 6 Newton s Lws of Motion Exple : Conservtive force : Grvittionl force, electric force, elstic force. Non conservtive force : rictionl force, viscous force. (5) Coon forces in echnics : (i) Weiht : Weiht of n object is the force with which erth ttrcts it. It is lso clled the force of rvity or the rvittionl force. (ii) ection or Norl force : When body is plced on riid surfce, the body experiences force which is perpendiculr to the surfces in contct. hen force is clled Norl force or ection. cos (iii) ension : he force exerted by the end of tut strin, rope or chin inst pullin (pplied) force is clled the tension. he direction of tension is so s to pull the body. = (iv) Sprin force : Every sprin resists ny ttept to chne its lenth. his resistive force increses with chne in lenth. Sprin force is iven by Kx ; where x is the chne in lenth nd K is the sprin constnt (unit N/). = Kx x 4.7 Equilibriu of Concurrent orce. () If ll the forces workin on body re ctin on the se point, then they re sid to be concurrent. () body, under the ction of concurrent forces, is sid to be in equilibriu, when there is no chne in the stte of rest or of unifor otion lon striht line. () he necessry condition for the equilibriu of body under the ction of concurrent forces is tht the vector su of ll the forces ctin on the body ust be zero. (4) Mtheticlly for equilibriu net 0 or x 0 ; y 0 ;, z 0 (5) hree concurrent forces will be in equilibriu, if they cn be represented copletely by three sides of trinle tken in order. C
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 7 (6) Li s heore : or concurrent forces sin sin sin Sple proble bsed on force nd equilibriu Proble 6. hree forces strts ctin siultneously on prticle ovin with velocity v. hese forces re represented in nitude nd direction by the three sides of trinle C (s shown). he prticle will now ove with velocity () v reinin unchned C Solution : () Proble 7. (b) Less thn v (c) Greter thn v (d) v in the direction of the lrest force C Given three forces re in equilibriu i.e. net force will be zero. It ens the prticle will ove with se velocity. wo forces re such tht the su of their nitudes is 8 N nd their resultnt is perpendiculr to the sller force nd nitude of resultnt is. hen the nitudes of the forces re [IEEE 00] () N, 6 N (b) N, 5N (c) 0 N, 8 N (d) 6 N, N Solution : (b) Let two forces re nd ( ). Proble 8. ccordin to proble: 8..(i) nle between nd resultnt () is 90 sin tn 90 cos cos 0 cos..(ii) nd cos 44 cos..(iii) by solvin (i), (ii) nd (iii) we et 5N nd N he resultnt of two forces, one double the other in nitude, is perpendiculr to the sller of the two forces. he nle between the two forces is [KCE (En./Med.) 00] () o 60 (b) o 0 (c) o 50 (d) Solution: (b) Let forces re nd nd nle between the is nd resultnt kes n nle with the force. sin tn tn 90 cos cos 0 cos / or 0 = o 90
8 8 Newton s Lws of Motion Proble 9. weihtless ldder, 0 ft lon rests inst frictionless wll t n nle of 60 o with the horizontl. 50 pound n is 4 ft fro the top of the ldder. horizontl force is needed to prevent it fro slippin. Choose the correct nitude fro the followin [CSE PM 998] () 75 lb (b) 00 lb (c) 70 lb (d) 50 lb Solution: (c) Since the syste is in equilibriu therefore x 0 nd y 0 nd W Now by tkin the oent of forces bout point..( C) W.( EC) ( C) [fro the fiure EC= 4 cos 60].( 0 sin 60) W(4 cos60) (0 cos60) s W 0 W 0 8W 8 50 70lb 0 0 Proble 0. ss M is suspended by rope fro riid support t P s shown in the fiure. nother rope is tied t the end Q, nd it is pulled horizontlly with force. If the rope PQ kes nle with the verticl then the tension in the strin PQ is Solution: (b) Proble. Solution: (c) () (b) (c) (d) sin / sin cos / cos ro the fiure or horizontl equilibriu sin sin sin sprin blnce shows redin of k, when n luiniu block is suspended fro it. nother blnce shows redin of 5 k, when beker full of liquid is plced in its pn. he two blnces re rrned such tht the l block is copletely iersed inside the liquid s shown in the fiure. hen [II-JEE () he redin of the blnce will be ore thn k (b) he redin of the blnce will be less thn 5 k (c) he redin of the blnce will be less thn k. nd tht of will be ore thn 5 k (d) he redin of blnce will be k. nd tht of will be 5 k. Due to buoynt force on the luiniu block the redin of sprin blnce will be less thn k but it increse the redin of blnce. Proble. In the followin dir, pulley P is ovble nd pulley P is fixed. he vlue of nle will be cos P v Q 6 ft 60 o M D E 4 ft W C Wll () 60 o (b) 0 o (c) 45 o (d) 5 o Solution: (b) ree body dir of pulley P is shown in the fiure or horizontl equilibriu cos cos nd W cos P W sin sin W W P cos
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 9 or verticl equilibriu sin sin W W sin W sin W sin or 0 Proble. In the followin fiure, the pulley is ssless nd frictionless. he reltion between, nd will be () (b) (c) W W P (d) Solution : (d) Since throuh sinle strin whole syste is ttched so W Proble 4. In the bove proble (), the reltion between W nd W will be Solution : () () W W (b) W cos cos (c) W W (d) W or verticl equilibriu W s W cos cos W cos W W W. cos cos W Proble 5. In the followin fiure the sses of the blocks nd re se nd ech equl to. he tensions in the strins O nd re nd respectively. he syste is in equilibriu with constnt horizontl force on. he is O cos cos W () (b) (c) (d) 5 Solution : (b) ro the free body dir of block cos (i) cos sin..(ii) by squrin nd ddin sin cos sin Proble 6. In the bove proble (5), the nle is Solution : (b) () 0 o (b) 45 o (c) 60 o (d) tn ro the solution (5) by dividin eqution(ii) by eqution (i) sin cos
0 0 Newton s Lws of Motion tn or 45 Proble 7. In the bove proble (5) the tension will be () (b) (c) (d) 5 Solution : (d) ro the free body dir of block or verticl equilibriu cos cos cos cos 45 cos cos..(i) or horizontl equilibriu sin sin sin 45 sin..(ii) by squrin nd ddin (i) nd (ii) equilibriu sin cos sin 5( ) or 5 Proble 8, In the bove proble (5) the nle will be Solution : (d) () 0 o (b) 45 o (c) 60 o (d) tn ro the solution (7) by dividin eqution(ii) by eqution (i) sin cos tn tn Proble 9. n of ss stnds on crte of ss M. He pulls on liht rope pssin over sooth liht pulley. he other end of the rope is ttched to the crte. or the syste to be in equilibriu, the force exerted by the en on the rope will be Solution : (b) () (M + ) (b) (c) M (d) (M ) ro the free body dir of n nd crte syste: or verticl equilibriu ( M ) ( M ) M (M + ) Proble 0. wo forces, with equl nitude, ct on body nd the nitude of the resultnt force is Solution : () nle between the two forces is () 7 cos (b) cos (c) cos 8 (d) cos 8 9 esultnt of two vectors nd, which re workin t n nle, cn be iven by cos [s nd ]. he
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion cos 9 cos 7 cos 9 7 7 cos or cos 8 8 Proble. cricket bll of ss 50 is ovin with velocity of /s nd is hit by bt so tht the bll is turned bck with velocity of 0 /s. he force of blow cts for 0.0s on the bll. he vere force exerted by the bt on the bll is Solution : () () 480 N (b) 600 N (c) 500 N (d) 400 N v / s nd v 0 / s [becuse direction is reversed] 50 0. 5k, t 0.0sec orce exerted by the bt on the bll 4.8 Newton s hird Lw. [ v v] 0.5[0 ( )] = 480 Newton t 0.0 o every ction, there is lwys n equl (in nitude) nd opposite (in direction) rection. () When body exerts force on ny other body, the second body lso exerts n equl nd opposite force on the first. () orces in nture lwys occurs in pirs. sinle isolted force is not possible. () ny ent, pplyin force lso experiences force of equl nitude but in opposite direction. he force pplied by the ent is clled ction nd the counter force experienced by it is clled ection. (4) ction nd rection never ct on the se body. If it were so the totl force on body would hve lwys been zero i.e. the body will lwys rein in equilibriu. (5) If = force exerted on body by body (ction) nd = force exerted on body by body (ection) hen ccordin to Newton s third lw of otion (6) Exple : (i) book lyin on tble exerts force on the tble which is equl to the weiht of the book. his is the force of ction. he tble supports the book, by exertin n equl force on the book. his is the force of rection. s the syste is t rest, net force on it is zero. herefore force of ction nd rection ust be equl nd opposite. (ii) Swiin is possible due to third lw of otion. (iii) When un is fired, the bullet oves forwrd (ction). he un recoils bckwrd (rection) (iv) eboundin of rubber bll tkes plce due to third lw of otion. (v) While wlkin person presses the round in the bckwrd direction (ction) by his feet. he round pushes the person in forwrd direction with n equl force (rection). he coponent of rection in horizontl direction kes the person ove forwrd. (vi) It is difficult to wlk on snd or ice. (vii) Drivin nil into wooden block without holdin the block is difficult. Sple proble bsed on Newton s third lw sin cos Proble. You re on frictionless horizontl plne. How cn you et off if no horizontl force is exerted by pushin inst the surfce
Newton s Lws of Motion Solution : (b) () y jupin (b) y splittin or sneezin (c) y rollin your body on the surfce (d) y runnin on the plne y doin so we cn et push in bckwrd direction in ccordnce with Newton s third lw of otion. 4.9 re of eference. () fre in which n observer is situted nd kes his observtions is known s his re of reference. () he reference fre is ssocited with co-ordinte syste nd clock to esure the position nd tie of events hppenin in spce. We cn describe ll the physicl quntities like position, velocity, ccelertion etc. of n object in this coordinte syste. () re of reference re of two types : (i) Inertil fre of reference (ii) Non-inertil fre of reference. (i) Inertil fre of reference : () fre of reference which is t rest or which is ovin with unifor velocity lon striht line is clled n inertil fre of reference. (b) In inertil fre of reference Newton s lws of otion holds ood. (c) Inertil fre of reference re lso clled unccelerted fre of reference or Newtonin or Glilen fre of reference. (d) Idelly no inertil fre exist in universe. or prcticl purpose fre of reference y be considered s inertil if it s ccelertion is neliible with respect to the ccelertion of the object to be observed. (e) o esure the ccelertion of fllin pple, erth cn be considered s n inertil fre. (f) o observe the otion of plnets, erth cn not be considered s n inertil fre but for this purpose the sun y be ssued to be n inertil fre. Exple : he lift t rest, lift ovin (up or down) with constnt velocity, cr ovin with constnt velocity on striht rod. (ii) Non inertil fre of reference : () ccelerted fre of references re clled non-inertil fre of reference. (b) Newton s lws of otion re not pplicble in non-inertil fre of reference. Exple : Cr ovin in unifor circulr otion, lift which is ovin upwrd or downwrd with soe ccelertion, plne which is tkin off. 4.0 Ipulse. () When lre force works on body for very sll tie intervl, it is clled ipulsive force. n ipulsive force does not rein constnt, but chnes first fro zero to xiu nd then fro xiu to zero. In such cse we esure the totl effect of force. () Ipulse of force is esure of totl effect of force. () I dt. t t (4) Ipulse is vector quntity nd its direction is se s tht of force. (5) Diension : [ ML ] (6) Units : Newton-second or K-- s (S.I.) nd Dyne-second or -c- s (C.G.S.) (7) orce-tie rph : Ipulse is equl to the re under -t curve. If we plot rph between force nd tie, the re under the curve nd tie xis ives the vlue of ipulse.
orce enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion I re between curve nd tie xis se Heiht t t ie (8) If v is the vere nitude of the force then I t t dt v t t dt v t d p (9) ro Newton s second lw dt t p or dt d p I p p p t p v t Ipulse t t t i.e. he ipulse of force is equl to the chne in oentu. his stteent is known s Ipulse oentu theore. (0) Exples : Hittin, kickin, ctchin, jupin, divin, collision etc. In ll these cses n ipulse cts. I dt v. t p constnt So if tie of contct t is incresed, vere force is decresed (or diluted) nd vice-vers. (i) In hittin or kickin bll we decrese the tie of contct so tht lre force cts on the bll producin reter ccelertion. (ii) In ctchin bll plyer by drwin his hnds bckwrds increses the tie of contct nd so, lesser force cts on his hnds nd his hnds re sved fro ettin hurt. (iii) In jupin on snd (or wter) the tie of contct is incresed due to yieldin of snd or wter so force is decresed nd we re not injured. However if we jup on ceented floor the otion stops in very short intervl of tie resultin in lre force due to which we re seriously injured. (iv) n thlete is dvised to coe to stop slowly fter finishin fst rce. So tht tie of stop increses nd hence force experienced by hi decreses. (v) Chin wres re wrpped in strw or pper before pckin. Sple proble bsed on Ipulse Proble. bll of ss 50 ovin with n ccelertion ipulsive force is 0 / s is hit by force, which cts on it for 0. sec. he () 0.5 N-s (b) 0. N-s (c) 0. N-s (d). N-s Solution : (c) Ipulsive force force tie t 0.5 0 0. = 0. N-s [MC 999] Proble 4. force of 50 dynes is cted on body of ss 5 which is t rest for n intervl of seconds, then ipulse is () 0.5 0 N - s (b) 0.98 0 N - s (c).5 0 N - s (d).5 0 N - s Solution : (c) Ipulse 5 force tie 50 0.5 0 N - s
orce (N) 4 4 Newton s Lws of Motion Proble 5. he force-tie ( t) curve of prticle executin liner otion is s shown in the fiure. he oentu cquired by the prticle in tie intervl fro zero to 8 second will be Solution : (d) () N-s (b) + 4 N-s (c) 6 N-s (d) Zero Moentu cquired by the prticle is nuericlly equl to the re enclosed between the -t curve nd tie xis. or the iven dir re in upper hlf is positive nd in lower hlf is netive (nd equl to the upper hlf). So net re is zero. Hence the oentu cquired by the prticle will be zero. + 4 6 8 ie (s) 4. Lw of Conservtion of Liner Moentu. If no externl force cts on syste (clled isolted) of constnt ss, the totl oentu of the syste reins constnt with tie. () ccordin to this lw for syste of prticles In the bsence of externl force 0 then p i.e., or p p p... constnt. p v v v... constnt d p dt constnt his eqution shows tht in bsence of externl force for closed syste the liner oentu of individul prticles y chne but their su reins unchned with tie. () Lw of conservtion of liner oentu is independent of fre of reference thouh liner oentu depends on fre of reference. () Conservtion of liner oentu is equivlent to Newton s third lw of otion. or syste of two prticles in bsence of externl force by lw of conservtion of liner oentu. p p constnt. v constnt. Differentitin bove with respect to tie dv dv 0 0 dt dt v 0 i.e. for every ction there is equl nd opposite rection which is Newton s third lw of otion. (4) Prcticl pplictions of the lw of conservtion of liner oentu (i) When n jups out of bot on the shore, the bot is pushed slihtly wy fro the shore. (ii) person left on frictionless surfce cn et wy fro it by blowin ir out of his outh or by throwin soe object in direction opposite to the direction in which he wnts to ove. (iii) ecoilin of un : or bullet nd un syste, the force exerted by trier will be internl so the oentu of the syste reins unffected. Let ss of un, ss of bullet, G v velocity of un, v velocity of bullet G Initil oentu of syste = 0 inl oentu of syste v G G v y the lw of conservtion liner oentu v G v
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 5 G v G So recoil velocity v 0 v G () Here netive sin indictes tht the velocity of recoil v G (b) v G G G v i.e. hiher the ss of un, lesser the velocity of recoil of un. is opposite to the velocity of the bullet. (c) While firin the un ust be held tihtly to the shoulder, this would sve hurtin the shoulder becuse in this condition the body of the shooter nd the un behve s one body. otl ss becoe lre nd recoil velocity becoes too sll. v G G n (iv) ocket propulsion : he initil oentu of the rocket on its lunchin pd is zero. When it is fired fro the lunchin pd, the exhust ses rush downwrd t hih speed nd to conserve oentu, the rocket oves upwrds. Let initil ss of rocket, 0 = ss of rocket t ny instnt t (instntneous ss) residul ss of epty continer of the rocket r u = velocity of exhust ses, v = velocity of rocket t ny instnt t (instntneous velocity) d rte of chne of ss of rocket = rte of fuel consuption dt = rte of ejection of the fuel. u u d () hrust on the rocket : u dt Here netive sin indictes tht direction of thrust is opposite to the direction of escpin ses. d u (if effect of rvity is nelected) dt (b) ccelertion of the rocket : u nd if effect of rvity is nelected d dt u d dt 0 (c) Instntneous velocity of the rocket : v u lo e t 0 0 nd if effect of rvity is nelected v u lo e.0 u lo 0 (d) urnt out speed of the rocket : v b v x u lo he speed ttined by the rocket when the coplete fuel ets burnt is clled burnt out speed of the rocket. It is the xiu speed cquired by the rocket. e Sple Proble bsed on conservtion of oentu Proble 6. won weihin 000 k is ovin with velocity 50 k/h on sooth horizontl rils. ss of 50 k is dropped into it. he velocity with which it oves now is 0 r v
6 6 Newton s Lws of Motion Solution : (c) ().5 k/hour (b) 0 k/hour (c) 40 k/hour (d) 50 k/hour Initilly the won of ss 000 k is ovin with velocity of 50 k/h So its oentu k k 000 50 h When ss 50k is dropped into it. New ss of the syste 000 50 50k Let v is the velocity of the syste. y the conservtion of liner oentu : Initil oentu = inl oentu 000 50 50 v 50,000 v 40k / h. 50 Proble 7. he kinetic enery of two sses nd re equl. he rtio of their liner oentu will be [PE 988] Solution : (c) () / (b) / (c) / (d) / eltion between liner oentu (P), n () nd kinetic enery (E) P E P [s E is constnt] P P Proble 8. Which of the followin hs the xiu oentu () 00 k vehicle ovin t 0.0 s (b) 4 weiht ovin t 0000 cs (c) 00 weiht ovin with kinetic enery 0 6 J (d) 0 weiht fter fllin kiloetre Solution : (d) Moentu of body for iven options re : () P v 00 0.0 k / sec (b) P v 4 0 00 0.4k / sec (c) P E 0. 0 6 6. 0 4 k / sec (d) P h 0 0 0 0 So for option (d) oentu is xiu. 4.8k / sec Proble 9. rocket with lift-off ss.5 0 k is blsted upwrds with n initil ccelertion of 0 / s. hen the initil thrust of the blst is () 5 5.75 0 N (b).5 0 N (c) 7.0 0 N (d) 4.0 0 N Solution : (c) Initil thrust on the rocket ( ).5 0 (0 0) 7.0 0 N Proble 0. In rocket of ss 000 k fuel is consued t rte of 40 k/s. he velocity of the ses ejected fro Solution : (c) the rocket is 5 0 () 4 / s. he thrust on the rocket is 0 N (b) 5 0 4 N (c) 0 6 N (d) 0 9 N hrust on the rocket ud 4 5 0 (40) 0 6 N dt Proble. If the force on rocket ovin with velocity of 00 /s is 0 N, then the rte of cobustion of the fuel is Solution : () () 0.7 k/s (b).4 k/s (c) 0.07 k/s (d) 0.7 k/s orce on the rocket 4 ud d 0 te of cobustion of fuel 0.7k / s. dt dt u 00 Proble. rocket hs ss of 00 k. 90% of this is fuel. It ejects fuel vpours t the rte of k/sec with velocity of 500 /sec reltive to the rocket. It is supposed tht the rocket is outside the rvittionl field. he initil upthrust on the rocket when it just strts ovin upwrds is [NCE 978] () Zero (b) 500 N (c) 000 N (d) 000 N 5 5 5
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 7 d Solution : (b) Up thrust force u dt 4. ree ody Dir. 500 500 N In this dir the object of interest is isolted fro its surroundins nd the interctions between the object nd the surroundins re represented in ters of forces. Exple : sin ree body dir of ss ree body dir of ss sin 4. pprent Weiht of ody in Lift. When body of ss is plced on weihin chine which is plced in lift, then ctul weiht of the body is. his cts on weihin chine which offers rection iven by the redin of weihin chine. his rection exerted by the surfce of contct on the body is the pprent weiht of the body. Condition iure Velocity ccelertion ection Conclusion LI Lift is t rest v = 0 = 0 Sprin lnce = 0 = pprent weiht = ctul weiht LI Lift ovin upwrd or downwrd with constnt velocity Sprin lnce v = constnt = 0 = 0 = pprent weiht = ctul weiht LI Lift ccelertin upwrd t the rte of ' Sprin lnce v = vrible < = = ( + ) pprent weiht > ctul weiht Lift ccelertin upwrd t the rte of LI v = vrible = = = pprent weiht = ctul weiht Sprin lnce
8 8 Newton s Lws of Motion LI Lift ccelertin downwrd t the rte of Sprin lnce v = vrible < = = ( ) pprent weiht < ctul weiht LI Lift ccelertin downwrd t the rte of Sprin lnce v = vrible = = = 0 pprent weiht = Zero (weihtlessness) Lift ccelertin downwrd t the rte of (>) LI Sprin lnce > v = vrible > = = = ve pprent weiht netive ens the body will rise fro the floor of the lift nd stick to the ceilin of the lift. Sple probles bsed on lift Proble. n weihs 80k. He stnds on weihin scle in lift which is ovin upwrds with unifor ccelertion of 5 / s. Wht would be the redin on the scle. ( 0 / s ) () 400 N (b) 800 N (c) 00 N (d) Zero Solution : (c) edin of weihin scle ( ) 80 (0 5) 00 N Proble 4. body of ss k is hun on sprin blnce ounted verticlly in lift. If the lift descends with n ccelertion equl to the ccelertion due to rvity, the redin on the sprin blnce will be () k (b) (4 ) k (c) ( ) k (d) Zero Solution : (d) ( ) ( ) 0 [becuse the lift is ovin downwrd with = ] Proble 5. In the bove proble, if the lift oves up with constnt velocity of /sec, the redin on the blnce will Solution : () e () k (b) 4 k (c) Zero (d) k Newton or k [becuse the lift is ovin with the zero ccelertion] Proble 6. If the lift in proble, oves up with n ccelertion equl to the ccelertion due to rvity, the redin on the sprin blnce will be () k (b) ( ) k (c) (4 ) k (d) 4 k Solution : (d) ( ) ( ) [becuse the lift is ovin upwrd with =] N 4 N or 4 k Proble 7. n is stndin on weihin chine plced in lift, when sttionry, his weiht is recorded s 40 k. If the lift is ccelerted upwrds with n ccelertion of will be ( 0 / s ) / s, then the weiht recorded in the chine () k (b) 40 k (c) 4 k (d) 48 k [MP PM 994]
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 9 Solution : (d) ( ) 40(0 ) 480 N or 48 k Proble 8. n elevtor weihin 6000 k is pulled upwrd by cble with n ccelertion of 5s. kin to be 0s, then the tension in the cble is [Mnipl MEE 995] () 6000 N (b) 9000 N (c) 60000 N (d) 90000 N Solution : (d) ( ) 6000 (0 5) 90, 000 N Proble 9. he rtio of the weiht of n in sttionry lift nd when it is ovin downwrd with unifor ccelertion is :. he vlue of is (- ccelertion due to rvity on the erth) Solution : (b) () (b) (c) weiht of n in sttionry lift weiht of n in downwrd ovin lift ( ) or Proble 40. 60 k n stnds on sprin scle in the lift. t soe instnt he finds, scle redin hs chned fro 60 k to 50 k for while nd then coes bck to the oriinl rk. Wht should we conclude () he lift ws in constnt otion upwrds (b) he lift ws in constnt otion downwrds (c) he lift while in constnt otion upwrds, is stopped suddenly (d) he lift while in constnt otion downwrds, is suddenly stopped Solution : (c) or retrdin otion of lift ( ) for downwrd otion ( ) for upwrd otion (d) Since the weiht of the body decrese for while nd then coes bck to oriinl vlue it ens the lift ws ovin upwrd nd stops suddenly. Note : Generlly we use ( ) for upwrd otion ( ) for downwrd otion here = ccelertion, but for the iven proble = retrdtion Proble 4. bird is sittin in lre closed ce which is plced on sprin blnce. It records weiht plced on sprin blnce. It records weiht of 5 N. he bird (ss = 0.5k) flies upwrd in the ce with n ccelertion of / s. he sprin blnce will now record weiht of [MP PM 999] Solution : (b) () 4 N (b) 5 N (c) 6 N (d) 7 N Since the ce is closed nd we cn tret bird ce nd ir s closed (Isolted) syste. In this condition the force pplied by the bird on the ce is n internl force due to this redin of sprin blnce will not chne. Proble 4. bird is sittin in wire ce hnin fro the sprin blnce. Let the redin of the sprin blnce be W. If the bird flies bout inside the ce, the redin of the sprin blnce is W. Which of the followin is true Solution : (b) () W W (b) W W (c) W W (d) Nothin definite cn be predicted In this proble the ce is wire-ce the oentu of the syste will not be conserved nd due to this the weiht of the syste will be lesser when the bird is flyin s copred to the weiht of the se syste when bird is restin is W W.
0 0 Newton s Lws of Motion 4.4 ccelertion of lock on Horizontl Sooth Surfce. () When pull is horizontl = nd = = / () When pull is ctin t n nle () to the horizontl (upwrd) + sin = = sin nd cos = cos () When push is ctin t n nle () to the horizontl (downwrd) = + sin nd cos = cos 4.5 ccelertion of lock on Sooth Inclined Plne. () When inclined plne is t rest Norl rection = cos orce lon inclined plne = sin = sin = sin () When inclined plne iven horizontl ccelertion b Since the body lies in n ccelertin fre, n inertil force (b) cts on it in the opposite direction. Norl rection = cos + b sin nd = sin b cos = sin b cos sin sin cos b cos +b sin Note : he condition for the body to be t rest reltive to the inclined plne : = sin b cos = 0 b = tn
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 4.6 Motion of locks in Contct. Condition ree body dir Eqution orce nd ccelertion f f f f f f f f f f f f C f f f f f ( ) f f f f C f f f f f f f f ( ) Sple probles bsed on otion of blocks in contct Proble 4. wo blocks of ss 4 k nd 6 k re plced in contct with ech other on frictionless horizontl surfce. If we pply push of 5 N on the hevier ss, the force on the lihter ss will be
Newton s Lws of Motion () 5 N (b) 4 N (c) N 5N 6 k 4 k (d) None of the bove Solution : (c) Let k, 4k nd 5N (iven) 6 orce on the lihter ss = 4 5 6 4 N Proble 44. In the bove proble, if push of 5 N is pplied on the lihter ss, the force exerted by the lihter ss on the hevier ss will be Solution : (d) () 5 N (b) 4 N (c) N (d) None of the bove orce on the hevier ss 6 5 N 6 4 Proble 45. In the bove proble, the ccelertion of the lihter ss will be Solution : () () 0.5 s (b) ccelerti on 5 Net force on the syste otl ss of the syste 4 s (c) 5 0 0.5 / s 5 6 s (d) None of the bove Proble 46. wo blocks re in contct on frictionless tble one hs ss nd the other s shown in fiure. orce is pplied on ss then syste oves towrds riht. Now the se force is pplied on. he rtio of force of contct between the two blocks will be in the two cses respectively. () : (b) : (c) : (d) : 4 Solution : (b) When the force is pplied on ss contct force When the force is pplied on ss contct force tio of contct forces f f f f
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 4.7 Motion of locks Connected by Mss Less Strin. Condition ree body dir Eqution ension nd ccelertion C ( ) C ( )
4 4 Newton s Lws of Motion Sple probles bsed on otion of blocks connected by ss less strin Proble 47. onkey of ss 0 k is holdin verticl rope. he rope will not brek when ss of 5 k is suspended fro it but will brek if the ss exceeds 5 k. Wht is the xiu ccelertion with which the onkey cn clib up lon the rope ( 0 / s ) Solution : (c) () 0 / s (b) 5 / s (c) Mxiu tension tht strin cn ber ( x) = 5 N = 50 N ension in rope when the onkey clib up.5 / s (d) 5 / s or liitin condition ( ) 50 x 0 0 50.5 / s Proble 48. hree blocks of sses k, k nd 5 k re connected to ech other with liht strin nd re then plced on frictionless surfce s shown in the fiure. he syste is pulled by force 0N, then tension [Oriss JEE 00] 0N k k 5k Solution : (c) () N (b) 5 N (c) 8 N (d) 0 N y coprin the bove proble with enerl expression. 5 0 8 5 Newton Proble 49. wo blocks re connected by strin s shown in the dir. he upper block is hun by nother strin. force pplied on the upper strin produces n ccelertion of / s in the upwrd direction in both the blocks. If nd be the tensions in the two prts of the strin, then [MU (En.) 000] () (b) (c) (d) 70. 8N nd 47. N 58. 8N nd 47. N 70. 8N nd 58. 8N 70. 8N nd 0 k 4k Solution : () ro..d. of ss 4 k 4 ' 4..(i) ro..d. of ss k '..(ii) or totl syste upwrd force 4 6 8 N = 70.8 N 4k 4 k by substitutin the vlue of in eqution (i) nd (ii) 4 nd solvin we et ' 47. N Proble 50. hree sses of 5 k. 0 k nd 5 k re suspended verticlly s shown in the fi. If the strin ttched to the support breks nd the syste flls freely, wht will be the tension in the strin between 0 k nd 5 k sses. ke 0 s. It is ssued tht the strin reins tiht durin the otion 5k 0k 5k
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 5 Solution : (d) () 00 N (b) 50 N (c) 50 N (d) Zero In the condition of free fll, tension becoes zero. Proble 5. sphere is ccelerted upwrds with the help of cord whose brekin strenth is five ties its weiht. he xiu ccelertion with which the sphere cn ove up without cord brekin is Solution : () () 4 (b) (c) (d) ension in the cord = ( + ) nd brekin strenth = 5 or criticl condition 5 4 his is the xiu ccelertion with which the sphere cn ove up with cord brekin. 4.8 Motion of Connected lock Over Pulley. Condition ree body dir Eqution ension nd ccelertion P 4 p [ ] + C 4[ ] [( ) ]
6 6 Newton s Lws of Motion Condition ree body dir Eqution ension nd ccelertion When pulley hve finite ss M nd rdius then tension in two seents of M strin re different M M M orque ) I ( ( ) ( ) I M M M M P P sin sin sin ( sin ) sin sin ( sin sin ) sin (sin sin ) sin
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 7 Condition ree body dir Eqution ension nd ccelertion sin sin sin P 4 d ( x ) dt d ( x s ) dt ccelertion of block ccelertion of block P (/ ) 4 4 4 C M ( ) [ M] ( M) [ M] M M ( M) M [ M]
8 8 Newton s Lws of Motion Sple probles bsed on otion of blocks over pulley Proble 5. liht strin pssin over sooth liht pulley connects two blocks of sses nd (verticlly). If the ccelertion of the syste is /8 then the rtio of the sses is [IEEE 00] () 8 : (b) 9 : 7 (c) 4 : (d) 5 : Solution : (b) = ; by solvin 9 / 7 8 Proble 5. block of ss 7 k is plced on frictionless tble. thred tied to it psses over frictionless pulley Solution : (b) nd crries body of ss k t the other end. he ccelertion of the syste is (iven = 0 s ) () (b) (c) (d) 00 s s 0s 0s 0 / s 7 [Kerl (En.) 000] Proble 54. wo sses nd re ttched to strin which psses over frictionless sooth pulley. When 0 k, 6 k, the ccelertion of sses is [Oriss JEE 00] Solution : (c) () 0 / s (b) 5 / s (c).5 / s (d) 0 / s 0 6 0.5 / s 0 6 Proble 55. wo weihts W nd W re suspended fro the ends of liht strin pssin over sooth fixed pulley. If the pulley is pulled up with n ccelertion, the tension in the strin will be 4WW WW WW WW () (b) (c) (d) W W W W W W ( W W ) Solution : () When the syste is t rest tension in strin If the syste oves upwrd with ccelertion then 4 4ww or w w Proble 56. wo sses M nd M re ttched to the ends of strin which psses over pulley ttched to the top of n inclined plne. he nle of inclintion of the plne in. ke = 0 s. If M = 0 k, M = 5 k, = 0 o, wht is the ccelertion of ss M () 0s (b) 5s 0 k 6 k (c) s (d) Zero sin 5 0. sin 0 5 5 Solution : (d) ccelertion = 0 5 0 5 0 Proble 57. In the bove proble, wht is the tension in the strin () 00 N (b) 50 N (c) 5 N (d) Zero M M
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 9 Solution : (b) sin 0 5 sin 0.0 50N 0 5 Proble 58. In the bove proble, iven tht M = M nd M oves verticlly downwrds with ccelertion. If the position of the sses re reversed the ccelertion of M down the inclined plne will be () (b) (c) / (d) None of the bove Solution : (d) If, then oves verticlly downwrd with ccelertion sin sin 0 = / If the position of sses re reversed then oves downwrd with ccelertion sin ' i.e. the will not ove. sin 0. 0 [s = ] Proble 59. In the bove proble, iven tht M = M nd the tension in the strin is. If the positions of the sses re reversed, the tension in the strin will be Solution : (c) () 4 (b) (c) (d) / sin ension in the strin If the position of the sses re reversed then there will be no effect on tension. Proble 60. In the bove proble, iven tht M = M nd Solution : (c) () 0s (b) sin sin 0 o 0 5s (c). Wht will be the ccelertion of the syste.5 / s [s = ] 4.5s (d) Zero o Proble 6. In the bove proble, iven tht M = M = 5 k nd 0. Wht is tension in the strin Solution : () () 7.5 N (b) 5 N (c).5 N (d) Zero sin 5 5 sin 0 0 7.5 N 5 5 Proble 6. wo blocks re ttched to the two ends of strin pssin over sooth pulley s shown in the fiure. he ccelertion of the block will be (in /s ) (sin 7 o = 0.60, sin 5 o = 0.80) Solution : (b) () 0. (b) 0. (c) (d) 0.066 sin sin 50 sin 5 00 sin 7 0. / s 00 50 Proble 6. he two pulley rrneents shown in the fiure re identicl. he ss of the rope is neliible. In () the ss is lifted up by ttchin ss to the other end of the rope. In (b). is lifted up by pullin the other end of the rope with constnt downwrd force of. he rtio of ccelertions in two cses will be Solution : (c) () : (b) : (c) : (d) : 4 or first cse..(i) () 00 k 50 k 7 o 5 o (b)
0 0 Newton s Lws of Motion or second cse fro free body dir of [s = ]..(ii) / ro (i) nd (ii) / Proble 64. In the djoinin fiure = 4. he pulleys re sooth nd liht. t tie t = 0, the syste is t rest. If the syste is relesed nd if the ccelertion of ss is, then the ccelertion of will be () (b) (c) (d) Solution : (d) Since the ss trvels double distnce in coprison to ss therefore its ccelertion will be double i.e. Proble 65. In the bove proble (64), the vlue of will be () (b) Solution : (c) y drwin the D of nd..(i)..(ii) by solvin these eqution / 4 Proble 66. In the bove proble, the tension in the strin will be Solution : (d) () (b) ro the solution (65) by solvin eqution (c) (c) 4 Proble 67. In the bove proble, the tie tken by in coin to rest position will be (d) (d) 8 () 0. s (b) 0.4 s (c) 0.6 s (d) 0.8 s Solution : (b) ie tken by ss to cover the distnce 0 c 0 () t h 0. 0. / 4.5 0.4 sec Proble 68. In the bove proble, the distnce covered by in 0.4 s will be () 40 c (b) 0 c (c) 0 c (d) 80 c Solution : () Since the ss cover double distnce therefore S = 0 = 40 c Proble 69. In the bove proble, the velocity cquired by in 0.4 second will be () 00 c/s (b) 00 c/s (c) 00 c/s (d) 400 c/s Solution : (b) Velocity cquired by ss in 0.4 sec 0 ro v u t [s / 5 / s ] v 0 5 0.4 / s 00 c / sec.
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion Proble 70. In the bove proble, the dditionl distnce trversed by in coin to rest position will be () 0 c (b) 40 c (c) 60 c (d) 80 c Solution : () When ss cquired velocity 00 c/sec it will ove upwrd till its velocity becoes zero. Proble 7. u 00 H 0 c 00 he ccelertion of block in the fiure will be () (b) (c) (d) ( 4 ) (4 ( ( 4 ) ) ) Solution : () When the block oves downwrd with ccelertion, the ccelertion of ss will be it covers double distnce in the se tie in coprison to. Let is the tension in the strin. y drwin the free body dir of nd..(i)..(ii) by solvin (i) nd (ii) 4 () becuse
Newton s Lws of Motion 4.9 Motion of Mssive Strin. Condition ree body dir Eqution ension nd ccelertion M M force pplied by the strin on the block ( M ) M M M ( M ) / M ension t id point of the rope M (M ) ( M ) L x / = Mss of strin = ension in strin t distnce x fro the end where the force is pplied [(L x)/l] L x L L x L L x (M/L)x Mx L M M = Mss of unifor rod L = Lenth of rod M x x M L L L x C Mss of seent C M x L L x L x L L
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 4.0 Sprin lnce nd Physicl lnce. () Sprin blnce : When its upper end is fixed with riid support nd body of ss hun fro its lower end. Sprin is stretched nd the weiht of the body cn be esured by the redin of sprin blnce W he echnis of weihin chine is se s tht of sprin blnce. Effect of fre of reference : In inertil fre of reference the redin of sprin blnce shows the ctul weiht of the body but in non-inertil fre of reference redin of sprin blnce increses or decreses in ccordnce with the direction of ccelertion [for detil refer rticle (4.)] () Physicl blnce : In physicl blnce ctully we copre the ss of body in both the pns. Here we does not clculte the bsolute weiht of the body. Here X nd Y re the ss of the epty pn. (i) Perfect physicl blnce : Weiht of the pn should be equl i.e. X = Y nd the needle ust in iddle of the be i.e. = b. Effect of fre of reference : If the physicl blnce is perfect then there will be no effect of fre of reference (either inertil or non-inertil) on the esureent. It is lwys errorless. (ii) lse blnce : When the sses of the pn re not equl then blnce shows the error in esureent. lse blnce y be of two types () If the be of physicl blnce is horizontl (when the pns re epty) but the rs re not equl X Y nd b or rottionl equilibriu bout point O X Yb (i) In this physicl blnce if body of weiht W is plced in pn X then to blnce it we hve to put weiht W in pn Y. or rottionl equilibriu bout point O ( X W) ( Y W ) b..(ii) Now if the pns re chned then to blnce the body we hve to put weiht W in pn X. or rottionl equilibriu bout point O ( X W ) ( Y W) b (iii) ro (i), (ii) nd (iii) rue weiht W W W X X O O b b Y Y
4 4 Newton s Lws of Motion (b) If the be of physicl blnce is not horizontl (when the pns re epty) nd the rs re equl i.e. X Y nd b In this physicl blnce if body of weiht W is plced in X Pn then to blnce it. We hve to put weiht W in Y Pn or equilibriu X W Y W..(i) Now if pns re chned then to blnce the body we hve to put weiht W in X Pn. or equilibriu ro (i) nd (ii) W rue weiht W W X W Y W..(ii) X O b Y Sple probles (Miscellneous) Proble 7. body weihs 8, when plced in one pn nd 8, when plced in the other pn of flse blnce. If the be is horizontl (when both the pns re epty), the true weiht of the body is () (b) (c) 5.5 (d) 5 Solution : (b) or iven condition true weiht = WW 8 8 =. Proble 7. plub line is suspended fro ceilin of cr ovin with horizontl ccelertion of. Wht will be the nle of inclintion with verticl [Oriss JEE 00] Solution : () () tn ( / ) ro the fiure tn tn / (b) tn ( / ) (c) cos ( / ) (d) cos ( / ) Proble 74. block of ss 5 k is ovin horizontlly t speed of.5 /s. perpendiculr force of 5 N cts on it for 4 sec. Wht will be the distnce of the block fro the point where the force strted ctin [Pb PM 00] Solution : () () 0 (b) 8 (c) 6 (d) In the iven proble force is workin in direction perpendiculr to initil velocity. So the body will ove under the effect of constnt velocity in horizontl direction nd under the effect of force in verticl direction. S x ux t.5 4 6 S t u t y y 0 / t 8 5 / 54 y S S x S 6 64 00 0 Proble 75. he velocity of body of rest ss 0 is this body is c (where c is the velocity of liht in vcuu). hen ss of [Oriss JEE 00]
enius PHYSICS by Prdeep Kshetrpl Newton s Lws of Motion 5 Solution : (c) () ( / ) 0 (b) ( / ) 0 (c) 0 (d) ( / ) 0 ro Einstein s forul 0 v c 0 0 0 Proble 76. hree weihts W, W nd W re connected to identicl sprins suspended for riid horizontl rod. he ssebly of the rod nd the weihts fll freely. he positions of the weihts fro the rod re such tht Solution : (c) () W will be frthest (c) ll will be t the se distnce C C 4 (b) W will be frthest (d) W will be frthest [oorkee 999] or W, W, W pprent weiht will be zero becuse the syste is fllin freely. So there will be no extension in ny sprin i.e. the distnces of the weiht fro the rod will be se. Proble 77. bird is sittin on stretched telephone wires. If its weiht is W then the dditionl tension produced by it in the wires will be Solution : (b) () = W (b) > W (c) < W (d) = 0 or equilibriu sin W W sin lies between 0 to 90 i.e. sin > W Proble 78. With wht iniu ccelertion cn firen slides down rope while brekin strenth of the rope is his weiht [CPM 979] () (b) (c) Solution : (c) When firen slides down, ension in the rope or criticl condition ( ) = / (d) Zero So, this is the iniu ccelertion by which firen cn slides down on rope. Proble 79. cr ovin t speed of 0 kilo eters per hour s is brouht to hlt in 8 etres by pplyin brkes. If the se cr is ovin t 60 k. per hour, it cn be brouht to hlt with se brkin power in () 8 etres (b) 6 etres (c) 4 etres (d) etres Solution : (d) ro v u s 0 u s u s s s u u s u (if = constnt) 60 4 s 4s 4 8 etres. 0 W sin