Question

Find the velocity of 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 $m_1=1kg,v_1=2\hat{i},$
$m_2=2kg,v_2=2\cos 30^{\circ }\hat{i}-2\sin 30^{\circ }\hat{j}$
$v_{CM}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}$
$=\frac{1\times 2i+2(2\cos 30^{\circ }\hat{i}-2\sin 30^{\circ }\hat{i})}{1+2}$
$=\frac{2\hat{i}+2\sqrt{3}\hat{i}-2\hat{j}}{3}$
$=\left(\frac{2+2\sqrt{3}}{3}\right)\hat{i}-\frac{2}{3}\hat{j}$