# Quiz , Work , Energy and Power

QUIZ TEST – I

Question :1 Two bodies of masses m1 and m2 have equal momenta. Their kinetic energies E1 and E2 are in the ratio:

(A) √m1 : √m2

(B) m1 : m2

(C) m2 : m1

(D) m12 : m22

Ans: (C)

Question:2 A chain of mass M, length l hangs from a pulley. If it is wound such that half of the chain remains overhung, the work done by the external agent is equal to

(A) Mgl/2

(B) (3/4)Mgl

(C ) (3/8)Mgl

(D) None of these

Ans: (C)

Question:3  A block of mass m is suspended by a light thread from an elevator. The elevator is accelerating upward with uniform acceleration a. The work done during t secs by the tension in the thread is:

(A)$\displaystyle \frac{m}{2}(g+a)a t^2$

(B) $\displaystyle \frac{m}{2}(g-a)a t^2$

(C) $\displaystyle \frac{m}{2}g a t^2$

(D) 0

Ans: (A)

Question:4 It is easier to draw up a wooden block along an inclined plane than to haul it vertically, principally because:

(A) the friction is reduced

(B) the mass becomes smaller

(C) only a part of the weight has to be overcome

(D) ‘g’ becomes smaller

Ans: (C)

Question:5  A motor boat is travelling with a speed of 3.0 m/sec. If the force on it due to water flow is 500 N, the power of the boat is:

(A) 150 KW

(B) 15 KW

(C) 1.5 KW

(D) 150 W

Ans: (C)

Question:6 Two masses of 1 gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is:

(A) 4 : 1

(B) √2 : 1

(C) 1 : 2

(D) 1 : 16

Ans: (C)

Question:7  A system of two bodies of masses m and M being interconnected by a spring of stiffness k moves towards a rigid wall with a K.E. E . If the body M sticks to the wall after the collision, the maximum compression of the spring will be

(A) $\displaystyle \sqrt{\frac{m E}{k}}$

(B) $\displaystyle \sqrt{\frac{2 m E}{(M+m)k}}$

(C) $\displaystyle \sqrt{\frac{2 m E}{M k}}$

(D)$\displaystyle \sqrt{\frac{2 M E}{(M+m)k}}$

Ans: (B)

Question:8  Two identical blocks each of mass m being interconnected by a light spring of stiffness k is pushed by a force F as shown in the figure. The maximum potential energy stored in the spring is equal to:

(A) F2/2K

(B) F2/4K

(C) F2/8K

(D) None of these

Ans: (A)

Question:9  A stone tied to a string of length l is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude in its velocity as it reaches a position, where the string is horizontal, is

(A) $\displaystyle \sqrt{u^2 – 2g l }$

(B) $\displaystyle \sqrt{ 2g l }$

(C) $\displaystyle \sqrt{u^2 – g l }$

(D)$\displaystyle \sqrt{2 (u^2 – g l) }$

Ans: (D)

Question:10  A cord is used to raise a block of mass m vertically through a distance d at a constant downward acceleration g/4. The work done by the chord is

(A) mgd/4

(B) 3Mgd/4

(C) -3Mgd/4

(D) Mgd

Ans: (B)

Question:11  A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part onto the table is:

(A) MgL

(B) MgL/3

(C) MgL/9

(D) MgL/18

Ans: (D)

Question:12  An engine pumps a liquid of density ‘d’ continuously through a pipe of area of cross-section A. If the speed with which the liquid passes through a pipe is v, then the rate of liquid flow is

Ans: (D)

Question:13 A body of mass m accelerates uniformly from rest to v1 in time t1. As a function of t, the instantaneous power delivered to the body is:

(A) mv1/t1

(B) mv12/t1

(C) mv1t2/ t1

(D) mv12t/t12

Ans: (D)

Question:14  A man M1 of mass 80 Kg runs up a staircase in 15 s. Another man M2 also of mass 80 Kg runs up the stair case in 20 s. The ratio of the power developed by them will be:

(A) 1

(B) 4/3

(C) 16/9

(D) None of the above

Ans: (B)

Question:15   How much work is done in raising a stone of mass 5 Kg and relative density 3 lying at the bed of a lake through height of 3 meter? (Take g = 10 ms-2):

(A) 25 J

(B) 100 J

(C) 75 J

(D) None of the above

Ans: (B)

Question:16  A person is pulling a mass m from ground on a rough hemispherical surface upto the top of the hemisphere with the help of a light inextensible string as shown in the figure. The radius of the hemisphere is R. The work done by the tension in the string is:

(A) mgR(1 + μ)

(B) μmgR

(C) mgR(1-μ)

(D) μmg(R/2)

Ans: (A)

Question:17  A small mass m is sliding down on a smooth curved incline from a height h and finally moves through a horizontal smooth surface. A light spring of force constant k is fixed with a vertical rigid stand on the horizontal surface, as shown in the figure. The maximum compression in the spring if the mass m released from rest from the height h and hits the spring on the horizontal surface is:

(A) $\displaystyle \sqrt{\frac{2 m g h}{k} }$

(B) $\displaystyle \sqrt{\frac{ m g h}{k} }$

(C) $\displaystyle \sqrt{\frac{ m g h}{2 k} }$

(D) None of these.

Ans: (A)

Question:18 A block of mass m moves towards a light spring of stiffness k on a smooth horizontal plane. If it compresses the spring through a distance x0 , the magnitude of total change in momentum of the block is:

(A) $\displaystyle 2 \sqrt{k m } x_0$

(B) 0

(C) $\displaystyle \sqrt{k m } x_0$

(D) $\displaystyle -2 \sqrt{k m } x_0$

Ans: (C)

Question:19  If v, P and E denote the velocity, momentum and kinetic energy of the particle, then:

(A) P = dE/dv

(B) P = dE/dt

(C) P = dv/dt

(D) none of these

Ans: (A)

Question:20  Energy required to accelerate a car from 10 to 20 m/s compared with that required to accelerate from 0 to 10 m/s is

(A) twice

(B) four times

(C) three times

(D) same