Question

Figure shows a fixed wedge on which two blocks of masses 2 kg and 3 kg are placed on its smooth inclined surfaces. When the two blocks are released from rest, the acceleration of centre of mass of the two blocks is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Block 'A' slides with acceleration $\frac{g}{2}$ and block 'B' slides with acceleration $\sqrt{3}\frac{g}{2}$.Now the acceleration of centre of mass of the system of blocks A and B can be given both in x and y directions as

${\overrightarrow{a}}_x=\frac{3\times \frac{\sqrt{3}g}{2}\left(cos{60}^{\circ }\right)-2\times \frac{g}{2}\left(cos{30}^{\circ }\right)}{5}=\frac{\sqrt{3}g}{20}\hat{i}$

and ${\overrightarrow{a}}_y=\frac{-[3\times \frac{\sqrt{3}g}{2}(sin{60}^{\circ })-2\times \frac{g}{2}(sin{30}^{\circ }\left)\right]}{5}=\frac{-11g}{20}\hat{j}$

Thus acceleration of the centre of mass of the system is given as

$a_{cm}=\sqrt{a_x^2+a_y^2}=\sqrt{(\frac{\sqrt{3}g}{20}{)}^2+(\frac{-11g}{20}{)}^2}=\frac{\sqrt{31}}{10}gm/s^2$