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Question

A long block A is at rest on a smooth horizontal surface. A small block B whose mass is half of mass of A is placed on A at one end and is given an initial velocity u as shown in Fig. 8.274. The coefficient of friction between the blocks is μ.
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A
Finally both move with a common velocity 2u/3.
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B
Acceleration of B relative to A initially is 3μg/2 towards left.
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C
Magnitude of total work done by friction is equal to the final kinetic energy of the system.
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D
The ratio of initial to final momentum of the system is 1.
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Solution

The correct options are
B Acceleration of B relative to A initially is 3μg/2 towards left.
D The ratio of initial to final momentum of the system is 1.
v is the final common velocity.
(m+2m)v=muv=u3
a1=μmgm=μg,a2=μmg2m=μg2
Acceleration of B relative to A:
a1+a2=μg+μg2
=32μg towards left
Work done against friction:
Wi=KiKf=12mu2123mv2=mu23
Final KE=123mv2=mμ26
Hence, c. is not correct.
Option (d) is correct because momentum is always conserved as there is no external force.
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