Question

Figure below 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, find the acceleration of centre of mass of the two blocks.

• A. $\frac{\sqrt{31}g}{10}$
• B. g
• C. g/2
• D. g/5

Answer 1

The correct option is A $\frac{\sqrt{31}g}{10}$

Block A slides with acceleration $\frac{g}{2}$ and block B slides with acceleration $\frac{\sqrt{3}g}{2}$. Now the acceleration of centre of mass of the system of blocks A and B can be given both in x and in y directions as
$a_x=\frac{3\times \frac{\sqrt{3}g}{2}cos{60}^{\circ }-2\times \frac{g}{2}sin{30}^{\circ }}{5}=\frac{\sqrt{3}g}{20}$
and $a_y=\frac{3\times \frac{\sqrt{3}g}{2}sin{60}^{\circ }+2\times \frac{g}{2}sin{30}^{\circ }}{5}=\frac{11g}{20}$
Thus acceleration of the centre of mass of the system is given as
$a_{CM}=\sqrt{a_x^2+a_y^2}=\sqrt{{\left(\frac{\sqrt{3}g}{20}\right)}^2+{\left(\frac{11g}{20}\right)}^2}=\frac{\sqrt{31}}{10}g$