Two bodies of masses m₁ = 5 kg and m₂ = 3 kg 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 m₁ will be : [Take g = 10ms^-2]

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30 N

60 N

40 N

50 N

answer is B.

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Detailed Solution

For equilibrium $m_{2} g = m_{1} gsin θ$
$\begin{array}{l} \sin θ = \frac{m_{2}}{m_{1}} = \frac{3}{5} \\ \cos θ = \frac{4}{5} \end{array}$
Normal force on $m_{1} = 5 gcos θ$
$= 5 \times 10 \times \frac{4}{5} = 40 N$

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