A plank P and block Q are arranged as shown on a smooth table top. They are given velocities 3 m/s and 6 m / s respectively. The length of plank is 1 m and block is of negligible size. After some time

Question

A plank P and block Q are arranged as shown on a smooth table top. They are given velocities 3 m/s and 6 m / s respectively. The length of plank is 1 m and block is of negligible size. After some time when the block has reached the other end of plank it stops slipping on plank. The velocity of plank then is (coefficient of friction between plank and block is 0.3 and mass of plank is double of block).

TestHub · Accepted Answer

No external horizontal force acts on plank + block, so linear momentum is conserved. Slipping stops when both reach a common velocity:

$m (6) + 2 m (3) = (m + 2 m) v \Rightarrow 12 m = 3 m v \Rightarrow v = 4 m/s$

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