A block A is placed over block B having mass m & 2 m respectively. Block B is resting on a frictionless surface and there is friction between block A and B . The system of blocks is pushed towards a s

Question

A block A is placed over block B having mass m & 2 m respectively. Block B is resting on a frictionless surface and there is friction between block A and B . The system of blocks is pushed towards a spring with a velocity $v_{0}$ such that A doesn't slip on B by the time the system comes to momentary rest. The correct statement is :-

TestHub · Accepted Answer

A does not slip, so the blocks move together and the spring absorbs their total kinetic energy:

$W_{spring} = - \frac{1}{2} (m + 2 m) v_{0}^{2} = - \frac{3}{2} m v_{0}^{2}$

Friction on A: $Δ K_{A} = - \frac{1}{2} m v_{0}^{2} \neq = 0$ . Friction on B: $Δ K_{B} - W_{spring} = - m v_{0}^{2} + \frac{3}{2} m v_{0}^{2} = + \frac{1}{2} m v_{0}^{2}$ . Only statement (C) is correct.

Ans. (C)

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