Question

Find the velocity of the centre of mass of the system shown in the figure.

• A. $\left(\frac{2 + 2 \sqrt{3}}{3}\right)\hat{i}-\frac{2}{3}\hat{j}$
• B. 4 $\hat{i}$
• C. $\left(\frac{2 - 2 \sqrt{3}}{3}\right)\hat{i}-\frac{1}{3}\hat{j}$
• D. None of these

Answer 1

Answer: (A)

Here, $m_{1}=1$ kg, $\overset{ \rightarrow }{v}_{1}=2\hat{i}$
$m_{2}=2kg$ , $\overset{ \rightarrow }{v}_{2}=2cos 30\hat{i}-2sin⁡30\hat{j}$
$\overset{ \rightarrow }{v}_{C M}=\frac{m_{1} \overset{ \rightarrow }{v}_{1} + m_{2} \overset{ \rightarrow }{v}_{2}}{m_{1} + m_{2}}$
$=\frac{1 \times 2 \hat{i} + 2 \left(\right. 2 cos 30 ^\circ \hat{i} - 2 sin ⁡ 30 ^\circ \hat{j} \left.\right)}{1 + 2}$
$=\frac{2 \hat{i} + 2 \sqrt{3} \hat{i} - 2 \hat{j}}{3}=\left(\frac{2 + 2 \sqrt{3}}{3}\right)\hat{i}-\frac{2}{3}\hat{j}$