A block of mass $m_{1}$ is in equilibrium on an inclined plane. Ignoring the friction at the pulley and mass of the string, the friction on the block is :

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(m_{2} g - m_{1} g \sin θ)

down the plane when

m_{2} > m_{1} \sin θ

Zero, when

m_{2} = m_{1} \sin θ

(m_{1} g \sin θ - m_{2} g)

up the plane when

m_{2} < m_{1} \sin θ

μ m_{1} gc o s θ

when

m_{2} \geq m_{1} (\sin θ + μ \sin θ)

answer is A, B, C, D.

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Detailed Solution

$1) If m_{2} < m_{1} \sin θ$

$f_{r} = m_{1} g \sin θ - m_{2} g$

Up the plane

$2) If m_{2} > m_{1} \sin θ$

$f_{r} = m_{2} g - m_{1} g \sin θ ↓$

$3) If m_{2} g = m_{1} g \sin θ$

$m_{2} = m_{1} \sin θ$

$f_{r} = 0$

$4) If m_{2} > m_{1} (\sin θ + μ \cos θ)$

$f_{r} = μ mg \cos θ$

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