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Two blocks of mass M and m are connected with a string which passes over a smooth pulley as shown in fig. The mass M is placed on a rough
inclined plane. The coefficient of friction between the block and the inclined plane is µ. What should be the minimum mass m so that the block M slides upward ?

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$m = M (\sin θ + μcos θ)$

$m = M (\sin θ - μcos θ)$

$m = \frac{M}{(\sin θ + μcos θ)}$

$m = \frac{M}{(\sin θ - μcos θ)}$

answer is A.

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Detailed Solution

For upward motion, both frictional force and the gravitational force acts down the plane.

$\begin{aligned} mg & \geq Mgsin θ + μMgcos θ \\ or & m & \geq M (\sin θ + μcos θ) \\ ∴ & (m)_{min} & = M (\sin θ + μcos θ) \end{aligned}$

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