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
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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
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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
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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
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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
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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
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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}}$
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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
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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) }$
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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
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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
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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
(A) Adv3/2
(B) (1/2) adv
(C) Adv2/2
(D) Adv2
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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
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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
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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
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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)
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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.
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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 $
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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
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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
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11. (D) 12. (D) 13. (D) 14. (B) 15. (B) 16. (A) 17. (A) 18. (C) 19. (A) 20. (C)