A double inclined plane as shown in the figure has fixed horizontal base and smooth faces with the same…
A double inclined plane as shown in the figure has fixed horizontal base and smooth faces with the same angle of inclination of $30^{\circ}$. A block of mass $300 \mathrm{~g}$ is on one face and is connected by a cord passing over a frictionless pulley to a second block of mass $200 \mathrm{~g}$ kept on another face. The acceleration with which the system of the blocks moves is ........ \% of acceleration due to gravity.
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Solution
From free body diagram
Adding Eqs (i) and (ii), we get
$
\begin{aligned}
& \left(m_2-m_1\right) g \sin \theta=\left(m_1+m_2\right) a \\
& \Rightarrow \quad a=\frac{(300-200) g \sin 30^{\circ}}{(300+200)} \\
& \Rightarrow \quad a=\frac{1}{10} g \\
& \therefore \quad a=10 \% \text { of } g \\
&
\end{aligned}
$
