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, ${\overrightarrow{v}}_1=2\hat{i}$
$m_2=2kg$ , ${\overrightarrow{v}}_2=2cos30\hat{i}-2sin30\hat{j}$
${\overrightarrow{v}}_{CM}=\frac{m_1{\overrightarrow{v}}_1+m_2{\overrightarrow{v}}_2}{m_1+m_2}$
$=\frac{1\times 2\hat{i}+2(2cos30^{\circ }\hat{i}-2sin30^{\circ }\hat{j})}{1+2}$
$=\frac{2\hat{i}+2\sqrt{3}\hat{i}-2\hat{j}}{3}=\left(\frac{2+2\sqrt{3}}{3}\right)\hat{i}-\frac{2}{3}\hat{j}$