Two bodies of masses $\mathrm{m}_1=5 \mathrm{~kg}$ and $\mathrm{m}_2=3 \mathrm{~kg}$ 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 $m_1$ will be. [Take $\left.g=10 \mathrm{~ms}^{-2}\right]$
Select the correct option:
A
30 N
B
40 N
C
50 N
D
60 N
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
For equilibrium $\mathrm{m}_2 \mathrm{~g}=\mathrm{m}_1 \mathrm{~g} \sin \theta$
$$
\begin{aligned}
& \sin \theta=\frac{m_2}{m_1}=\frac{3}{5} \\
& \sin \theta=\frac{4}{5}
\end{aligned}
$$
Normal force on $\mathrm{m}_1=5 \mathrm{~g} \cos \theta$
$$
=5 \times 10 \times \frac{4}{5}=40 \mathrm{~N}
$$
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