Question

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 $300g$ is on one face and is connected by a cord passing over a frictionless pulley to a second block of mass $200g$ kept on another face. The acceleration with which the system of the blocks moves is w.... \% of acceleration due to gravity.

• A. 5
• B. 10
• C. 15
• D. 20

Answer 1

Answer: (B)

From free body diagram
$T-m_{1}g\sin \theta =m_{1}a$ ... (i)
and $m_{2}g\sin \theta -T=m_{2}a$ ...(ii)
Adding Eqs (i) and (ii), we get
$\left(m_2-m_1\right)g\sin \theta =\left(m_1+m_2\right)a$
$\Rightarrow a=\frac{(300-200)g\sin 30^{\circ }}{(300+200)}$
$\Rightarrow a=\frac{1}{10}g$
$\therefore a=10\%$ of $g$