Two bodies of masses m₁ = 5 kg and m₂ = 3 kg are connected by a light… | JEE Main 2022 (29 Jul, Shift 2)

Q19JEE Main 2022 · 29 JUL · SHIFT 2Easy

Connected Bodies & Pulleys

Two bodies of masses $m_1 = 5\text{ kg}$ and $m_2 = 3\text{ kg}$ 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 $m_1$ will be: [Take $g = 10\text{ ms}^{-2}]$

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Answer: (b)

At rest: tension $T = m_2 g = 3 \times 10 = 30\text{ N}$ .
For $m_1$ along the smooth incline: $T = m_1 g\sin\theta \Rightarrow 30 = 50\sin\theta \Rightarrow \sin\theta = \frac{3}{5}$ , $\cos\theta = \frac{4}{5}$ .
The incline (smooth) exerts only the normal force: $N = m_1 g\cos\theta = 50 \times \frac{4}{5} = 40\text{ N}$ .
So the answer is (b) 40 N.

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