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A smooth plank of mass 1kg and length 8m Is on smooth horizontal surface. The gap between fixed pulley P and plank is larger than the length of plank. A smooth block D is placed on the plank. The masses of blocks A and B are 1kg and 3kg, respectively. Find the time elapsed before the block D separates from the plank.

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Detailed Solution

$a = \frac{m_{B} g - m_{A} g}{m_{A} + m_{B} + m_{C}} = \frac{20}{5} = 4 m / s^{2} s = \frac{1}{2} a t^{2} or \sqrt{\frac{8 \times 2}{4}} = t t = 2 s$

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