Work, Energy and Power

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Q161. A long sprig when stretched by x cm has a potential energy V. on increasing the stretching to nx cm, the potential

energy stored in the spring will be

(a) v/n (b) nv (c) n2v (d) v/n

2

Q162. Two bodies of masses m and 4m are moving with equal kinetic energy. The ratio of their linear momentum is

(a) 1 : 4 (b) 4 : 1 (c) 1 : 2 (d) 1 : 1

Q163. Two bodies of masses m and 4m are moving with equal linear momentum. The ratio of their kinetic energies is

(a) 1 : 4 (b) 1 : 1 (c) 4 : 1 (d) 1 : 2

Q164. The relationship between the force F and

position x of a body is as shown in figure. The

work down in displacing the body from x = 1m to

x = 5m. will be

1 2 3 4 5 6O

-5

-10

5

10

F(N)

x (m)

(a) 20 J (b) 15 J (c) 25 J (d) 30 J

Q165. Several forces varying both in magnitude and direction are used to move a particle along a smooth curved horizontal

path. The work done in the particle by the resultant force equals the change in the

(a) total energy of the particle

(b) kinetic energy of the particle

(c) potential energy of the particle

(d) any of the above depending upon the nature of forces and path.

Q166. A body of mass m accelerates uniformly from rest to a speed u in a time T. The instantaneous power delivered to the

body as a function of time t is given by

(a) tT

mu

2

1 2

(b) tT

mu

2

12

2

(c) tT

mu2

2

(d) 2

2

2

tT

mu

Q167. The gain in potential energy of an object of mass M raised from the surface of the earth to a height equal to the radius

R of the earth is

(a) MgR/2 (b) MgR (c) 2MgR (d) MgR/4

Q168. Two mass M and 4M are suspended from the ends of two identical springs. Both the masses are stretched down from

their mean positions and let go simultaneously. If they are in same phase every four seconds, the springs constant is

(a) π N/m (b) π2N/m (c) 2πN/m (d) 2π2

N/m

Q169. Ten springs of spring constant 1 N/m, ½ N/m, ¼ N/m---- connected in

parallel as shown are equivalent to a single spring of spring constant.

(a) 45 N/m (b) 511/256 N/m

(c) 12.3 N/m (d) 1023/512 N/m

m

Q170. The force required to stretch a spring varies with distance stretched as

shown If the experiment is performed with a spring of half the length, the

line OA will

(a) shift towards F−axis (b) shift towards X−axis

(c) remain unchanged (d) becomes double the length

F(N)

2

0.04 x (m)

Q171. The period of oscillation of the spring system of spring constant 120 N. m is T. If an other spring of spring constant

240 N/m is connected in series with this spring the time period of the system will become.

(a) √3 T (b) 2/3 T (c) 3T (d) √3/2 T


Q172. Two bodies of masses M1 and M2 have same kinetic energy. The ratio of their linear momentum is

(a) 21 M/M (b) 12 M/M (c) M1/M2 (d) M2/M1

Q173. Two bodies of unequal masses moving with velocity V1 and V2 have same kinetic energy. The ratio of their linear

momentum is

(a) V1/V2 (b) V2/V1 (c) 21 V/V (d) 12 V/V

Q174. A man raises to 10 bricks to the top of a building by going up a vertical spiral stair case in ? whereas a boy raises to

bricks to the same spot by a straight ladder in 10 minutes. Then

(a) neither of their does any work (b) both of their does any work

(c) the boy does more work their the man (d) the boy does less work their the man

Q175. A weight w extends the spring of length L by a length � . If the spring is cut into halves, the same weight will produce

the extension equal to

(a) 2/� (b) � (c) 2 � (d) � /√2

Q176. A sphere of mass m1 in motion hits directly another sphere of mass m2 and sticks to it. The total kinetic energy after the

collision is 2/3 of their initial kinetic energy. The ratio of m1 : m2 is

(a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) 2 : 3

Q177. Three particles are projected vertically upwards from a point on the surface of the earth with velocities

3

gR2, gR ,

3

gR4 respectively where R is the radius of the earth and g, the acceleration due to gravity on its

surface. If the maximum heights attained are respectively h1, h2, h3, then

(a) h1 : h2 = 2 : 3 (b) h2 : h3 = 3 : 4 (c) h1 : h3 = 1 : 2 (d) h2 = R

Q178. The potential energy of a particle of mass 5 kg moving in the XY plane is given by V = −7x + 24 y J (X, Y in metres).

Initially at t = 0, the particle is at the origin moving with a velocity 6 [(2.4) i + (0.7) j ] m/s which of the statements

below is false

(a) Velocity of the particle at t = 4 is 25 m/s

(b) Acceleration of the particle is 5 m/s2

(c) The direction of motion of the particle at t = 0 is perpendicular to the direction of its acceleration

(d) The path is particle is a circle

Q179. Two masses of 1 g and 4 g are moving with kinetic energies in the ratio 4 : 1. The ratio of their linear momenta is

(a) 1 : 1 (b) 1 : √2 (c) 4 : 1 (d) 16 : 1

Q180. Two identical cylinders of area of cross−section A level contain liquid of density ρ. The level of liquid in one is h1 and

in other in h2 (h2 > h1). When the two cylinder are connected, the work done by gravity to equilise the levels in the two

cylinders is proportion to

(a) 1/4 ρS (x2 − x1) (b) 1/4 ρS (x2 − x1)2 (c) 4 ρS (x2 − x1) (d) 4 ρS (x2 − x1)

2

Q181. A block of mass m slides down from rain of the hemispherical bowl of radius R along its inner surface. The velocity of

the block at bottom will be

(a) gR (b) gR2 (c) gRπ (d) gR2

Q182. The work done by the string of a simple pendulum during one complete oscillation is equal to

(a) Total energy of the pendulum (b) Kinetic energy of the pendulum

(c) Potential energy of the pendulum (d) zero

Q183. If the kinetic energy of a body becomes four time its initial value, its momentum will

(a) increase to four times (b) decrease by four times (c) increase to two times (d) decrease by two times

Q184. The kinetic energy of a body of mass M as it slide

down the incline shown below is 10 J. The mass of the

body is (g = 10 m/s2)

2m

30

(a) 1 kg (b) 2 kg (c) √2 kg (c) 2√2 kg


Q185. A body is released from the top of a tower. After one second its kinetic energy is K. After one more second its kinetic

energy will be

(a) k (b) 2k (c) 4k (d) 8k

Q186. A body is released from the top of a tower. After one second its potential energy decreases by P. After one more

second it will decrease by

(a) p (b) 2p (c) 4p (d) 8p

Q187. The bob of a simple pendulum is at its mid point, its energy is

(a) half kinetic and half potential (b) totally potential

(c) totally kinetic (d) zero

Q188. When the bob of a simple pendulum is at its extremes position, its energy is

(a) zero (b) half kinetic and half potential

(c) totally potential (d) totally kinetic

Q189. From a water fall, water is pouring down at the rate of 100 kg/sec. on the blades of a turbine. If the height of fall is 100

m, the power delivered to the turbine is approximately equal to

(a) 1 kw (b) 10 kw (c) 100 kw (d) 1000 kw

Q190. When a body of mass m revolves with a uniform speed v on a circular path of radius r, the work done by the body in

one complete rotation is

(a) 1/2 mv2 (b) 2πmv

2 (c)

−π

2

12 mv

2 (d) zero

Q191. A particle moves in a circle of radius R with a constant speed under the centripetal force F. The work done in

completing a full circle is

(a) zero (b) 2πRF (c) πR2F (d) πRF

Q192. The power of an engine required to lift 200 kg of iron are per second from a mine 6m deep is nearly

(a) 120 w (b) 1200 w (c) 12 kw (d) 20 kw

Q193. A shell at rest explodes into three fragments. Two of three move at right angle to each other. The third fragment will

move in a direction

(a) at right angles to both the above (b) along the resultant of the two

(c) opposite to the resultant of the two (d) determined at random

Q194. A stone is tied to a rope and attached to a wooden bar which rotates at a constant angular velocity. Suddenly the bar is

stopped and the stone gets encircled around the bar. The angular velocity of the stone

(a) increases (b) decreases

(c) remains constant (d) first increase and then decrease

Q195. A lead ball and a tennis ball of equal mass strike a wall with the same velocity. The former falls down and the latter

bounces back. Which of the following statements about their momenta is correct ?

(a) The lead ball has greater momentum than the tennis ball

(b) both the balls suffer same change in momentum

(c) the lead ball suffers greater change in momentum

(d) the tennis ball suffers greater change in momentum

Q196. A double−decker bus is unlikely to topple over while moving round a curve if

(a) all the passengers are on the upper deck (b) there are no passengers on the two decks

(c) passengers are equally divided on the two decks

(d) all the passengers are on the lower deck

Q197. A body at rest disintegrate into two pieces of equal mass. The two pieces will move in

(a) the same direction with equal speeds (b) the same direction with unequal speeds

(c) the opposite direction with equal speeds (d) the opposite direction with unequal speeds

Q198. The work done in joules in increasing the extension of an elastic spring of stiffness 200 N/m from 5 cm to 15 cm is

(a) 5 (b) 3 (c) 2 (d) 1

Q199. Two spheres of masses 3 kg and 2 kg collide directly. Their relative velocity before collision is 15 m/s and after

collision in 5 m/sec. The loss of kinetic energy in joule due to collision is

(a) 500 (b) 350 (c) 220 (d) 120

Q200. The period of simple pendulum in a stationery lift is T. When the lift has an upward acceleration of 159/49, the period

of oscillation of the pendulum will be


(a) 15 T/49 (b) 49 T/15 (c) 7T/8 (d) T

Q201. A shell of mass 2m fired with a speed v at an angle θ to the horizontal explodes at the highest point of its motion into

two fragments of mass m each. If one fragment where initial speed in zero vertically, the distance at which the other

fragment falls from the gun is given by

(a) g

2sinu

2

3 2 θ (b)

g

2sinu2 2 θ (c)

g

2sinu 2 θ (d)

g

2sinu3 2 θ

Q202. If the earth were to contract suddenly to 1/n th of its present size without any change in mass, the duration of the new

day will be nearly

(a) 24/h hours (b) 24/n2 hours (c) 24 n hours (d) 24 n

2 hours

Q203. Sand is dropping from a stationery hopper on to a conveyer belt at a rate given by dM/dt, the force required to keep the

belt moving at a constant speed v is

(a) dt

dMv 2 (b)

dt

dM

v

1 (c)

dt

dM

v

12

(d) dt

dMv

Q204. A bird in a wire cage hangs from a spring balance. The reading of the balance is taken when the bird is flying about in

the cage and a second when the bird is at rest in the cage. The first reading will be

(a) much greater than the second (b) slightly greater than the second

(c) less than the second (d) the same as the second

Q205. A thick moves on a smooth horizontal surface with a uniform speed u carrying stone dust. If a mass ∆m of the

stone−dust leaks from the truck in a time ∆t, the force needed to keep the truck moving at its uniform speed is

(a) u ∆m/∆t (b) ∆m (du/dt) (c) dt

dum

t

mu ∆+

∆∆

(d) zero

Q206. Three particles each of mass m are located at the vertices of an equilateral triangle ABC. They start moving with equal

speeds v each along the medium of the triangle and collide at its centered G. If after the collision, A comes to rest and B

retraces is path along GB, then C,

(a) also comes to rest (b) moves with a speed v along CG

(c) moves with a speed v along BG (d) moves with a speed v along AG

Q207. A body of mass M moving with a speed u has a ‘heat−on’ collision with a body of mass m originally at rest. If M >>

m, the speed of the body of mass in after the collision will be nearly

(a) u (m/M) (b) u (M/m) (c) u/2 (d) 2u

Q208. Two particles 1 & 2 of equal mass moving with velocity v1 and v2 respectively make an elastic head on collision. After

the collisions, the particles 1 & 2 have their velocities equal to

(a) v1 and v2 (b) zero each

(c) v2 and v1 (d) any combination consistent with conservation of energy

Q208. In the above problem if the particle (2) is at rest initially, the velocity of particles 1 & 2 after the collision will be

(a) v1 and 0 (b) zero each (c) v1 each (d) 0 and v1

Q209. A particle of small mass moving with velocity v collide with a very heavy body at rest, the velocities of the particle and

the body after the collision will be

(a) 0 and v (b) v and 0 (c) −v and zero (d) zero and −v

Q210. A particle A suffers an oblique collision with a particle B, that is at rest initially. If their masses are same, then after the

collision.

(a) they will move in opposite direction

(b) A will continue to more in the original direction while B remains at rest

(c) they will move in mutually perpendicular direction

(d) A comes to rest and B starts moving in the direction of the original motion of A

Q211. During the oscillations of a simple pendulum the kinetic energy of the simple pendulum also varies periodically with

frequency wk. Its relationship with the frequency of the pendulum is

(a) wk = w/2 (b) wk = w (c) wk = 2w (d) no relationship

Q212. The potential energy of a simple pendulum varies with frequency wp during the motion of a simple pendulum. Wp is

related to the frequency w of the pendulum as

(a) wp = w/2 (b) wp = w (c) wp = 2w (d) no relation

Q213. The kinetic energy and potential energies of a simple pendulum vary periodically during the motion the pendulum. The

total energy of the pendulum


(a) also varies with the same periodicity as that of the kinetic energy

(b) also varies with the same periodicity as that of the potential energy

(c) also varies with same periodicity as that of the pendulum

(d) remains constant

Q214. A body of mass M is dropped from a height h above the earths surface which of the following statements is not true for

this body

(a) The kinetic energy of the body increases and is equal to Mgh just before it strikes the ground

(b) The velocity of the body just before it strike the ground is gh2

(c) the potential energy of the body remain constant during the fall

(d) the gain in kinetic energy is equal to the work done by gravitational force on the body during its false

Q215. Springs A and B are identical except that A is stiffer than B. If they are stretched by the same amount

(a) work expended on A is more than that on B

(b) work expended on A is same as that on B

(c) work expended on A is less than that on B

(d) the work done on each will depend upon the duration of the application of force

Q216. Springs A and B are identical except that A is stiffer than B. If they are stretched by the same force

(a) work expended on A is more that ht on B

(b) work expended on A is less than that on B

(c) work expended on A is equal to that on B

(d) work expended on each will depend upon the duration of the application of force

Q217. A hollow metallic sphere filled with water is used as bob of a simple pendulum. If the sphere has a small hole in the

bottom through which the water is leaking continuously, the time period of the pendulum will

(a) gradually go on increasing

(b) gradually go on decreasing

(c) remain unchanged

(d) gradually go on increasing initially and will increase later when the sphere is empty

Q218. A cricket ball is hit at an angle of 45° to the ? with a kinetic energy W. At the highest point kinetic energy is

(a) E (b) E/2 (c) E/√2 (d) zero

Q219. The bob A of a pendulum released from 30° to the vertical hits another

bob B of the same mass at rest on a table as shown. After the collision

bob A will

(a) turn back and rise to its initial height

(b) turn back and rise to height les than its initial height

(c) rises to the same height on the other side

(d) come to rest and transfer all the moment to other ?

30°

m

Am

Q220. Pair production in the process in which a quantum of electromagnetic radiation in field of a nucleus produces a pair of

electron and position. For the process which of the statements below is false

(a) It exhibits equivalence of mass−energy

(b) It exhibits violation of conservation of mass as two massive particles are creates

(c) It exhibits law of conservation of momentum as the massive particles share the momentum of the radiation

(d) The process can take place only for certain minimum energy of the radiation

Answers

161. (c): def.

162. (c): kE = p2/2m

163. (b)

164. (c): w = Fx cosθ

165. (b): def.

166. (c): Power = Energy/time

167. (a): The attractive force = −GMm/r2 work done by the force to more the body from R to 2R position

168. (b): def. F = kx

169. (b): definition − addition of spring force in parallel


170. (a)

171. (b): def−addition of springs in series

172. (a): kE = p2/2m

173. (b)

174. (b): work done against gravity is equal

175. (a)

176. (c): conservation of energy−momentum

177. (d): kE will be zero at max. height

178. (d): nothing can said about the path from the data

179. (a): as above relation between kE & P

180. (b): work done = Gravitation force × height

181. (d): KE = PE at the position

182. (d): conservation force

183. (c)

184. (a): KE = PE at the bottom

185. (c): def.

186. (c): def.

187. (c): at the mean position PE = 0

188. (c): at the extreme position KE = 0

189. (c): Power = Energy/time

190. (d): def.

191. (a): centripetal force is normal to displacement

192. (c): def.

193. (c): conservation of linear momentum

194. (b): conservation of energy−momentum

195. (d)

196. (d): centre of gravity is lowest


198. (c): def.

199. (d)

200. (c)

201. (a): conservation of linear momentum and energy

202. (b)

203. (d): Linear momentum conservation

204. (c): Gravity does not act on the balance when the bird is flying

205. (d): conservation of linear momentum


207. (d): collision problem = conservation of linear momentum/energy

208. (c): as above

208. (d): as above

209. (c): as above

210. (c): collision problem

211. (c): in one cycle KE goes to zero twice

212. (c): in one cycle PE give to zero twice

213. (d): PE + KE remain constant

214. (c)

215. (a): w = 2

1 kx

2

216. (b): F = kx, w = 2

1 kx

2 =

2

1 k . F

2/k

2

217. (d): centre of gravity shift down ? and then upward after the water has completely

218. (d): def.

219. (d): collision problem − conservation of energy − linear momentum.


220. (b): conservation of energy into mass E = mc2.

Work, Energy and Power

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