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 the above

Answer 1

The Correct Option is A

Here, $m_{1}=1 \,kg , \overrightarrow{ v _{1}}=2 \hat{ i }$ $m_{2} =2 kg \overrightarrow{\vec{v}_{2}}=2 \cos 30 \hat{ i }-2 \sin 30 \hat{ j } $ $\vec{v}_{ cm } =\frac{m_{1} \overrightarrow{ v }_{1}+m_{2} \overrightarrow{ v _{2}}}{m_{1}+m_{2}} $ $=\frac{1 \times 2 \hat{i}+2(2 \cos 30 \hat{i}-2 \sin 30 \hat{i}}{1+2} $ $=\frac{2 \hat{i}+2 \sqrt{3} \hat{i}-2 \hat{j}}{3}$ $=\left(\frac{2+2 \sqrt{3}}{3}\right) \hat{i}-\frac{2}{3} \hat{j}$