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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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