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 $300\, g$ is on one face and is connected by a cord passing over a frictionless pulley to a second block of mass $200\, g$ 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 $g$