Question

Two bodies of masses $10kg$ and $2kg$ are moving with velocities $2\hat{i}-7\hat{j}+3\hat{k}$ and $-10\hat{i}+35\hat{j}-3\hat{k}m/s$ respectively. The velocity of the centre of mass of the two - body system is:-

• A. 0.21
• B. 0.2
• C. 0.15
• D. 0.1

Answer 1

The correct option is B 0.2

$\begin{array}{c}For{m}_1=1.0kg,\\ Velocity,{\overrightarrow{v}}_1=\left(-1.5\cos {37}^0\hat{i}-1.5\sin {37}^0\right)=-1.2\hat{i}-0.9\hat{j}\\ For{m}_2=1.2kg,\\ Velocity,{\overrightarrow{v}}_2=0.4\overrightarrow{j}\\ For{m}_3=1.5kg,\\ Velocity,{\overrightarrow{v}}_3=-1.0\cos {37}^0\overrightarrow{i}+1.0\sin {37}^0\hat{j}\\ For{m}_4=0.50kg,\\ Velocity,{\overrightarrow{v}}_4=3.0\hat{i}\\ For{m}_5=1.0kg\\ Velocity,{\overrightarrow{v}}_5=2.0\cos {37}^0\hat{i}-2.0sin{37}^0\hat{j}\\ \left(\cos {37}^0=\frac{4}{5}and\sin {37}^0=\frac{3}{5}\right)\\ V_{cm}=\frac{m_1{\overrightarrow{v}}_1+m_2{\overrightarrow{v}}_2+m_3{\overrightarrow{v}}_3+m_4{\overrightarrow{v}}_4+m_5{\overrightarrow{v}}_5}{m_1+m_2+m_3+m_4+m_5}\\ =\frac{1}{1.0+1.2+1.5+1.0+0.50}\left[1.0\left(-1.5\times \frac{4}{5}\overrightarrow{i}-1.5\times \frac{3}{5}\overrightarrow{j}\right)+.....-2.0\times \frac{3}{5}\overrightarrow{j}\right]\\ Onsolvingtheaboveequation,weget\\ V_{cm}is0.20m/s\\ Hence,\\ optionBiscorrectanswer.\end{array}$