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The figure shows an L shaped body of mass M placed on smooth horizontal surface. The block A is connected to the body by means of an inextensible string, which is passing over a smooth pulley of negligible mass. Another block B of mass m is placed against a vertical wall of the body. Find the minimum value of the mass of block A so that block B remains stationary relative to the wall. Coefficient of friction between the block B and the vertical wall is $μ$ .

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$\frac{(M + m)}{μ - 3}$

$\frac{(M + m)}{μ - 2}$

$\frac{(M + m)}{μ}$

$\frac{(M + m)}{μ - 1}$

answer is D.

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Detailed Solution

$a = \frac{m_{1} g}{m_{1} + M + m} For the equilibrium of B, m g = μ N = μ (m a) = \frac{μ m m_{1} g}{m_{1} + M + m} ∴ m_{A} = \frac{(M + m) m}{(μ - 1) m} m_{A} = \frac{(M + m)}{μ - 1}$

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