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Two bodies of masses $\mathrm{m_{1}=5 \mathrm{~kg} \: and \: m_{2}=3 \mathrm{~kg}}$ 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 $\mathrm{m}_{1}$ will be : [Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ]

Option: 1
$30 \mathrm{~N}$

Option: 2
$40 \mathrm{~N}$

Option: 3
$50 \mathrm{~N}$

Option: 4
$60 \mathrm{~N}$

Answers (1)

best_answer

For a system at rest

$\mathrm{m_{1}g\cos \theta =N}\rightarrow (1)$

( $\mathrm{N\rightarrow }$ Force by inclined plane on the block)

$\mathrm{T=m_2 g=30 N \rightarrow(2) }$

$\mathrm{m _{1} g \sin \theta=T }$

$\mathrm{50 \sin \theta=30 }$

$\mathrm{\sin \theta=\frac{3}{5} }$

$\mathrm{\theta=37^{\circ} }$

$\mathrm{N=m_1 g \cos \theta }$

$\mathrm{=50 \times \cos 37^{\circ} }$

$\mathrm{N=40 N}$

The force exerted by the inclined plane on the body of mass $\mathrm{m_1}$ will be $\mathrm{40 \mathrm{~N}}$

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