Question

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

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

Answer 1

Answer: (A)

Here $m_1=1 \, kg, v_1=2 \hat {i},$
$m_2=2\,kg,v_2=2 \, \cos 30^{\circ} \hat {i}-2\sin \, 30^{\circ} \hat {j}$
$v_{CM}= \frac {m_1v_1+m_2v_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} $