Q.
Two blocks of masses $m$ and $2m$ are connected by a light string passing over a frictionless pulley. As shown in the figure, the mass $m$ is placed on a smooth inclined plane of inclination $30{^\circ}$ and $2m$ hangs vertically. If the system is released, the blocks move with an acceleration equal to
A) $\frac{g}{4}$
B) $\frac{g}{3}$
C) $\frac{g}{2}$
D) $g$
Explanation
(c) $As\ 2m > m$
The acceleration of the two block system will be as shown in figure.
[image:5_image217.jpeg]
The equation for block of mass $2m\ $is
$2mg - T = 2ma$ …(i)
Similarly, for block of mass $m$
$T - mg\sin{30{^\circ} = ma}\ $…(ii)
From Eqs. (i) and (ii), we have
$2mg - \frac{mg}{2} = 3ma$
$\Longrightarrow \ \ a = \frac{g}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.