Question

A boy and a block, both of same mass, are suspended at the same horizontal level, from each end of a light string that moves over a frictionless pulley as shown. The boy starts moving upwards with an acceleration 2.5 $m / s^{2}$ relative to the rope. If the block is to travel a total distance l0 m before reaching at the pulley, the time taken by the block in doing so is equal to:

Moderate

Solution

If u be the velocity of the boy relative to the rope and v (upward) be the velocity of the block relative to the ground ,then conserving linear momentum , m(u-v0+m(-v) = 0 $\Rightarrow v = \frac{u}{2} \Rightarrow a_{b l o c k} = \frac{a_{b o y}}{2} \Rightarrow a_{b l o c k} = \frac{2.5}{2} m / s^{2} = 1.25 m / s^{2} H e n c e t i m e r e q u i r e d f o r t h e b l o c k = \sqrt{\frac{2 h}{a_{b l o c k}}} = \sqrt{\frac{2 \times 10}{1.25}} s = 4 s$

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