Question

# A block of mass 'm' and a pan of equal mass are connected by a string going over a smooth light pulley as shown in figure. Initially the system is at rest when a particle of mass m falls on the pan and sticks to it. If the particle strikes the pan with a speed 'v' find the speed with which the system moves just after the collision.

A

v/2

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B

v/3

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C

v/6

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D

2v/3

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Solution

## The correct option is B v/3 Let the required speed be V. As there is a sudden change in the speed of the block, the tension must change by a large amount during the collision. Let N = magnitude of the contact force between the particle and the pan T = tension in the string Consider the impulse imparted to the particle. The force is N in upward direction and the impulse is ∫ N dt. This is equal to the change in its momentum. Thus, ∫ N dt = mv − mV ......................(i) Similarly for the pan: ∫ (N − T) dt = mV ................(ii) And for the block: ∫ T dt = mV ................(iii) Adding (ii) and (iii), ∫ N dt = 2mV Comparing with (i), mv mV = 2mV Therefore, V = v3

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