Question

A body of mass $m_1=4kg$ moves at $5\hat{i}m/s$ and another body of mass $m_2=2kg$ moves at $10\hat{i}m/s$. The kinetic energy of centre of mass is :

• A. $\frac{200}{3}J$
• B. $\frac{500}{3}J$
• C. $\frac{400}{3}J$
• D. $\frac{800}{3}J$

Answer 1

The correct option is C $\frac{400}{3}J$

$v_{CM}=\frac{m_1\frac{d{r}_1}{dt}+m_2\frac{d{r}_2}{dt}}{m_1+m_2}$
$=\frac{4\times 5\hat{i}+2\times 10\hat{i}}{4+2}$
$v_{CM}=\frac{40\hat{i}}{6}=\frac{20}{3}\hat{i}$
The kinetic energy
$K=\frac{1}{2}m{v}^2$
$=\frac{1}{2}\times (4+2)\times \frac{20\times 20}{3\times 3}$
$=\frac{1}{2}\times 6\times \frac{20\times 20}{3\times 3}$
$K=\frac{400}{3}J$.