Question

Two bodies of 6 kg and 4 kg masses have their velocity $5\hat{i}-2\hat{j}+10\hat{k}$ and $10\hat{i}-2\hat{j}+5\hat{k}$ respectively. Then the velocity of their centre of mass is

• A. $5\hat{i}+2\hat{j}-8\hat{k} $
• B. $7\hat{i}+2\hat{j}-8\hat{k} $
• C. $7\hat{i}-2\hat{j}+8\hat{k} $
• D. $5\hat{i}-2\hat{j}+8\hat{k} $

Answer 1

Answer: (C)

Here, $m_1 = 6\, kg, m_2 = 4 \,kg$
$\vec{\upsilon_{1}}=5\hat{i}-2\hat{j}+10\hat{k}$
$\vec{\upsilon_{2}}=10\hat{i}-2\hat{j}+5\hat{k}$
The velocity of the centre of mass is
$\vec{\upsilon}_{CM}=\frac{m_{1}\vec{\upsilon_{1}}+m_{2}\vec{\upsilon_{2}}}{m_{1}+m_{2}}$
$=\frac{\left(6\right)\left(5\hat{i}-2\hat{j}+10\hat{k}\right)+4\left(10\hat{i}-2\hat{j}+5\hat{k}\right)}{6+4}$
$=\frac{30\hat{i}-12\hat{j}+60\hat{k}-8\hat{j}+20\hat{k}}{10}$
$=\frac{70\hat{i}-20\hat{j}+80\hat{k}}{10}=7\hat{i}-2\hat{j}+8\hat{k}$