Question

Two blocks A and B each of equal masses 'm' are released from the top of a smooth fixed wedge as shown in the figure. The magnitude of acceleration of the centre of mass of the two blocks is ___.

Answer 1

Let us consider incline surfaces of wedge as x-axis and y-axis respectively. We can write accelerations of blocks A and B.
${\overrightarrow{a}}_A=mgsin{30}^{\circ }\hat{i}and{\overrightarrow{a}}_B=mgsin{60}^{\circ }\hat{j}$
The acceleration of centre of mass of two blocks can be written as
${\overrightarrow{a}}_{am}=\frac{m_A{\overrightarrow{a}}_A+m_B{\overrightarrow{a}}_B}{m_A+m_B}=\frac{mgsin{30}^{\circ }\hat{i}+mgsin{60}^{\circ }\hat{j}}{m+m}$
$=\frac{gsin{30}^{\circ }\hat{i}+mgsin{60}^{\circ }\hat{j}}{m+m}$
$=\frac{g}{4}\hat{i}+\frac{\sqrt{3}g}{4}\hat{j}\Rightarrow \left|{\overrightarrow{a}}_{am}\right|=\frac{g}{2}$