Question

At $t=0$, the position and velocities of two particle are as shown in the figure. They are kept on a smooth surface and being mutually attracted by gravitational force. Find the position of center of mass at $t=2s$.

• A. $X=5m$
• B. $X=7m$
• C. $X=3m$
• D. $X=2m$

Answer 1

Answer: (B)

$X=7m$

$X_{cm}=r_{cm}=\frac{10\hat{i}+0\hat{i}}{2}=5\hat{i}$
$V_{cm}=\frac{5\hat{i}-3\hat{i}}{2}=\frac{2\hat{i}}{2}=1\hat{i}$
Sum of external force is zero.
$a_{cm}=0$
$V_{cm}=$ constant
After $2$ sec
Distance travelled $=2\times 1=2\hat{i}$
Final $X$ of centre of mass $=2\hat{i}+5\hat{i}$
$=7\hat{i}$
So, $=7m$