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James Fowler
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1 Work Power Energy. For conservaive orce ) Work done is independen o he pah ) Work done in a closed loop is zero ) Work done agains conservaive orce is sored is he orm o poenial energy 4) All he above. Two springs have heir orce consans k and k and hey are sreched o he same exension. I k > k work done is ) Same in boh he springs ) More in spring K ) More in spring K 4) None. Two springs have heir orce consans k and k (K >K ). When hey are sreched by he same orce, work done is ) Same in boh he springs ) More in spring K ) More in spring K 4) None 4. A lorry and a car moving wih same KE are brough o res by applying he same rearding orce. Then ) Lorry will come o res in a shorer disance ) Car will come o res in a shorer disance ) Boh come o re in he same disance 4) None 5. A lorry and a car moving wih same momenum are brough o res by applying he same rearding orce. Then ) Lorry will come o res in a shorer disance) Car will come o res in a shorer disance ) Boh come o re in he same disance 4) None 6. When a wound spring is dissolved in an acid, he emperaure o he acid ) Increases ) Decreases ) Remains same 4) None 7. A body is moved along a sraigh line by a machine delivering consan power. The disance moved by he body in ime is proporional o ) ) 4 ) 4)

2 8. A) Work done by ricional orce is always negaive. B) A body a res can have mechanical energy. C) Mechanical energy o reely alling body decrease gradually. ) Only A is rue ) Only B is rue ) Only C is rue 4) All he hree one rue 9. Mach he pairs in wo liss given below. Lis - I Lis - II a) Graviaional orce e) Decreases b) Fracional orce ) Conservaive orce c) KE o a dropped body g) Non-Conservaive orce d) PE o a dropped h) Increases body ) a-, b-h, c-g, d-e ) a-, b-g,c-h,d-e ) a-,b-g,c-e,d-h 4) a-h, b-g,c-,d-e 0. A body is allowed o all rom a heigh h above he ground. Then mach he ollowing. Lis - I Lis - II a) PE=KE e) A heigh h/ b) PE=KE ) Consan a any poin c) KE = PE g) A heigh h/ d) PE +KE h) A heigh h/ ) a-e, b-g,c-h,d- ) a-g,b-e,c-,d-h ) a-, b-g,c-e,d-h 4) a-e,b-h,c-g,d-. A): When a person is walking horizonally wih a suicase on his head, no work is done by him agains graviaional orce. R): Graviaional orce on suicase acs verically downwards and moion is in horizonal direcion, hence do produc becomes zero. ) Boh (A) and (R) are rue and (R) is he correc explanaion o (A). ) Boh (A) & (R) are rue bu (R) is no correc explanaion o (A). ) (A) is rue and (R) is alse. 4) (A) is alse bu (R) is rue.

3 . A) Work done by graviaional orce in moving a body is pah independen. R) Graviaional orce is non conservaive orce. ) Boh (A) and (R) are rue and (R) is he correc explanaion o (A). ) Boh (A) & (R) are rue bu (R) is no correc explanaion o (A). ) (A) is rue and (R) is alse. 4) (A) is alse bu (R) is rue.. A block o mass 'm' is lowered wih he help o a rope o negligible mass hrough a g disance 'd' wih an acceleraion o. Work done by he rope on he block is ) Mgd Mgd ) ) Mgd Mgd 4) 4. A orce F= (5iˆ ˆj+ kˆ ) N moves a paricle rom r ˆ = (iˆ+ 7 ˆj+ 4 k) m o r ˆ = (5iˆ+ ˆj+ 8 k) m. The work done by he orce is ) 8J ) 8J ) 8J 4) 48J 5. A uniorm chain o lengh m is kep on a able such ha a lengh o 60 cm hangs reely rom he edge o he able. The oal mass o he chain is 4 kg. Wha is he work done in pulling he enire chain on o he able? (g = 0 m/s ) ) 7.J ).6J ) 0J 4) 00J 6. n idenical cubes each o mass m and side l are on he horizonal surace. Then he minimum amoun o work done o arrange hem one on he oher is ) nmgl ) mgl n ) mgl n( n ) 4) mgl n( n + ) 7. A recangular block o dimensions 6m x 4m x m and o densiy.5 gm/c.c is lying on horizonal ground wih he ace o larges area in conac wih he ground. The work done in arranging i wih is smalles area in conac wih he ground is, (g=0ms ) ) 880 kj ) 440 kj ) 800 kj 4) 70 kj 8. A ladder 'AB' o weigh 00N and lengh 5m is lying on a horizonal surace. Is cenre o graviy is a a disance o 'm' rom end A. A weigh o 80N is aached a end B. The work done in raising he ladder o he verical posiion wih end 'A' in conac wih he ground is ) 500J ) 000J ) 50J 4) 900J

4 ^ ^ 9. Force acing on a paricle is i+ j N. Work done by his orce is zero, when a paricle is moved along he line y+kx = 5. Here he value o k is ) ) 4 ) 6 4) 8 0. A body o mass 6kg is under a orce which causes displacemen in i which is given by s= m, where is ime. The work done by he orce in s is 4 ) J ) 9 J ) 6 J 4) J. A paricle o mass 00g is hrown verically upwards wih a speed o 5 m/s. The work done by he orce o graviy during he ime he paricle goes up is (g = 0ms ) ) 0.5J ).5J ).5J 4) 0.5J. A paricle is projeced a 60 0 o he horizonal wih a kineic energy K. The kineic energy a he highes poin is ) K ) Zero ) K/4 4) K/. I he kineic energy o a body is our imes is momenum, is velociy is ) ms ) 4 ms ) 8 ms 4) 6 ms 4. A.0 HP moor pumps ou waer rom a well o deph 0m and ills a waer ank o volume 8 lires a a heigh o 0m rom he ground. The running ime o he moor o ill he empy ank is (g = 0 ms ) ) 5 min ) 0 min ) 5 min 4) 0 min 5. A ball is projeced verically down wih an iniial velociy rom a heigh o 0m on o a horizonal loor. During he impac i loses 50% o is energy and rebounds o he same heigh. The velociy o projecion is (g = 0ms ) ) 0 ms ) 5 ms ) 0 ms 4) 5 ms 6. A sone is projeced verically up o reach a maximum heigh 'h'. The raio o is kineic o poenial energies a a heigh 4 will be 5h ) 5: 4 ) 4: 5 ) : 4 4) 4:

5 7. A block o mass 'm' is conneced o one end o a spring o 'spring consan' k. The oher end o he spring is ixed o a rigid suppor. The mass is released slowly so ha he oal energy o he sysem is hen consiued by only he poenial energy, hen d is he maximum exension o he spring. Insead, i he mass is released suddenly rom he same iniial posiion, he maximum exension o he spring now is: (g acceleraion due o graviy) ) mg k ) mg k ) d 4) 4d 8. A moor o power P 0 is used o deliver waer a a cerain rae hrough a given horizonal pipe. To increase he rae o low o waer hrough he same pipe n imes, he power o he moor is increased o P. The raio o P o P 0 is ) n : ) n : ) n : 4) n 4 : 9. One ourh chain is hanging down rom a able. Work done o bring he hanging par o he chain on o he able is (mass o chain=m and lengh = L) ) MgL ) MgL 6 ) MgL 8 4) MgL 4 0. A ladder 'AB'.5m long and o weigh 50N wih is cenre o mass a a disance m rom end 'A' is on he ground. A 40N weigh is aached o he end B. The work o be done o arrange he ladder in verical posiion wih end 'A' conac wih he ground is ) 90J ) 50J ) 85J 4) 475J. A body o mass m is acceleraed uniormly rom res o a speed v in a ime T. The insananeous power delivered o he body as a uncion o ime, is given by ) mv T ) mv T ) T mv 4) T mv. A locomoive o mass m sars moving so ha is velociy varies as v=k S, where K is a consan and S is he disance raversed. The oal work done by all he orces acing on he locomoive during he irs second aer he sar o moion is ) mk4 ) 4 mk4 ) 8 mk4 4) 6 mk4

6 . A paricle o mass 'm' is projeced wih a velociy 'u' a an angle 'α ' wih he horizonal. Work done by graviy during is descen rom is highes poin o, he posiion where is velociy vecor makes an angle α wih he horizonal is, ) mu an ) α mu an ) mu cos Tan α α α 4) mu cos sin 4. A uniorm chain o mass 'm' and lengh 'L' is kep on a horizonal able wih hal o is lengh hanging rom he edge o he able. Work done in pulling he chain on o he able so ha only h o is lengh now hangs rom he edge is, 5 ) mgl 8 mgl ) 50 mgl ) 8 α 4) mgl A small block o mass 'm' is kep on a rough inclined surace o inclinaion θ ixed in an elevaor. The elevaor goes up wih a uniorm velociy V and he block does no slide on he wedge. The work done by he orce o ricion on he block in a ime will be ) Zero ) mgv cos θ ) mgv sin θ 4) mgv sinθ 6. A recangular plank o mass 'm ' and heigh 'a' is on a horizonal surace. On he op o i anoher recangular plank o mass 'm ' and heigh 'b' is placed. The poenial energy o he sysem is ( a+ b) ( m+ m ) g ) m + m. b a+ m g ) m b ) + m a+ m g m b 4) + m a+ m g 7. A box o mass 50kg a res is pulled up on an inclined plane m long and m high by a consan orce o 00N. When i reaches he op o he inclined plane i is velociy is ms, he work done agains ricion in Joules is (g = 0ms ) ) 50 ) 00 ) 50 4) 00

7 8. Two idenical cylindrical vessels each o area o cross secion A are on a level ground. Each conains a liquid o densiy ''. The heighs o liquid columns are h and h. I he wo vessels are conneced by means o a narrow pipe a he boom, he work done by graviy in equalizing he liquid levels is ) ( ) Aρ g h h Aρ g h h Aρ g h h 4 ) ( ) ) ( ) A ρ g h h 4 4) ( ) 9. An open knie edge o mass M is dropped rom a heigh 'h' on a wooden loor. I he blade peneraes a disance s ino he wood, he average resisance oered by he wood o he blade is h ) Mg ) Mg + s ) Mg h s 4) h Mg + s 40. A shell o mass 'm' moving horizonally explodes in o wo equal pieces a he insan is momenum is 'p'. One o he ragmens aains a linear momenum o '4p' in upward direcion. The kineic energy gained by he sysem immediaely aer explosion is ) 5p m ) 6 p m 4. A spring o orce consan 'k' is sreched by a small lengh 'x'. The work done in sreching i urher by a small lengh 'y' is ) ( ) ) 4p m 4) 7p m k x + y ) ( ) k x+ y ) ( ) k y x 4) ( ) ky x+ y 4. A body is projeced verically up wih cerain velociy. A a poin 'P' in is pah, he raio o is poenial o kineic energies is 9: 6. The raio o velociy o projecion o velociy a 'P' is ) : 4 ) 5: 4 ) 9: 5 4) 5: 6 4. When a body is projeced verically up, a a poin 'P' in is pah, he raio o poenial o kineic energies is : 4. I he same body were o be projeced wih wo imes he iniial velociy, he raio o poenial o kineic energies a he same poin is ) : 5 ) : 8 ) : 0 4) : 5

8 44. A unirom chain o lengh 'L' is placed on a smooh able o heigh 'h' (h > L) wih a lengh '' hanging rom he edge o he able. The chain begins o slide down he able. When he end o he chain is abou o leave he edge o he able is velociy is ) g( L+l) L ) g( L l) L ) g L L ( l ) 4) g( L l) 45. A bulle o mass 0 gm is ired horizonally wih a velociy o 000 ms rom a heigh o 50m above he ground. I he bulle reaches he ground wih a velociy o 500 ms, he work done agains air resisance in Joules is (g = 0ms ) ) 5005 ) 755 ) 750 4) 7.5 Key ) 4 ) ) 4) 5) 6) 7) 8) 9) 0) ) ) ) 4) 5) 6) 7) 8) 9) 0) 4 ) ) ) 4) 5) 6) 7) 8) 9) 0) ) ) ) 4) 4 5) 6) 7) 8) 4 9) 40) 4 4) 4 4) 4) 44) 45)

9 Hins. W = -m ( g - a ).d g = -m g -.d W = - mgd 4. S = r - r S = i -5j + 4k F = 5 i -j + k W = F.S = = 8 J m.g. l 5. W =.6Joules = n 6. PE = ( ) i l nm. g. nl PE = ( nm). g W = P.E mgl P.Ei W = n ( n ) 7. m = d.v =.5 x 000 x 48 P.E i = mg. W = P.E P.E i and = 440 KJ 8. W = 00 x + ( 80 x 5 ) = 000 J 9. F = i + j Tanθ = = m K y + kx = 5 Y = - 5 x + K m = - m m = - 6 P.E = mg.

10 k = K = 0. S = 4 V = = 4 u = 0 V = ms mv J W = = = W = - mgh = - mu J = = K = mu θ mu = K cos K = K.cosθ = K.cos 60 K = 4 K mv = 4mv v = 8 ms - mgh P = 746 = = 900s = 5 min = + mgh mu mgh u = gh = 0 0 = 0 ms 4h P. E = mg. 5 4h mgh P. E = mgh mg = 5 5 K. E.: P. E = : 4 7. mg k = d

11 mgx = kx or mgd mg x = d d k = mg = 8. P = V υ = A P α V Adυ P = n P 9. W = mgl = mgl = mgl n x 4 0. W = = = 50J. P = F.V = ma ( a) = V P = m. ma dv k k. a =. v =. k s = dx s F = ma = and S = a 4 m. a K W = = m. 8 v r. Kγ = i 0 an α = u cos α α v y = u.cosα.an α kv cos an = mu α α W = ky ky cos an i = mu α l 4. W = mg n n W = mgl 00

12 5. W = x s = sin θ. V = mg sinθ.sinθ. v. W = mg.sinθ.v a 6. u = m g u b = m g a + m b = + + u. oal m a m g W = F x L - mgh + mυ = 00 x - 50 x 0 x + x50 00J = Aρg u = h + h u = A g h + h ρ Aρg W = u - u = h h 4 [ ] 9. Mg ( h + s) = F. S F Mg h = + s 40. ( p) i ( 4 P). j P Gain in K. ε = + P = 5P 6P 5P 9P = + m m m 4. ( ) W = K x + y - Kx K W =.y x + y ( ) 7P = m 4. h 9 = H - h 6 5h u H 5 H = 9 υ = H h = 4

13 4. P k = u = u, n = 4 P P = = k n P + K P + 4 ( ) ( ) = 5 l l 44. PE = Mx. g. L L and PE = Mg K. E. = P. E P. E L Mgl Mυ = Mg υ = L ( l ) g L 45. Work done agains air Resisance m( u gh) mυ = + = 755 J L

1. VELOCITY AND ACCELERATION

1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under