A block of mass \( m \) and a pan of equal mass are connected by a string going over a smooth li....

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A block of mass \( m \) and a pan of equal mass are connected by a string going over a smooth light pulley. 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
\( \mathrm{P} \)
with which the system moves just after the collision.
(1) \( \frac{v}{2} \)
(2) \( \frac{v}{3} \)
(3) \( \frac{v}{4} \)
(4) \( v \)


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