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Two bodies of masses $m_{1} = 5 k g$ and $m_{2} = 3 k g$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $m_{1}$ will be: $[T a k e g = 10 m s^{- 2}]$

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$50 N$

$60 N$

$30 N$

$40 N$

answer is B.

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Detailed Solution

For equilibrium condition, $m_{2} g = m_{1} g \sin θ$

$\sin θ = \frac{m_{2}}{m_{1}} = \frac{3}{5} \cos θ = \frac{4}{5}$

Normal force (N) on $1 = 5 g \cos θ$

$= 5 \times 10 \times \frac{4}{5} = 40 N$

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