Question

At $t=0$ the positions and velocities of two particles are as shown in the figure. They are kept on a smooth surface and being mutually attracted by gravitational force. Then the position of the centre of mass at $t=2s$ is

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

Answer 1

Answer: (B)

Initial position of center of mass,
$x_i=\frac{1\left(0\right)+1\left(10\right)}{1+1}=5m$
Initial velocity of center of mass,
$v=\frac{1\left(5\right)+1\left(-3\right)}{1+1}=1m$
This velocity remains constant as the internal forces during collision do not change the velocity of the center of mass. Therefore distance travelled by the center of mass in $2s$ ,
$\Delta x=v\Delta t$
$\Delta x=1\left(2\right)=2m$
Final position of center of mass,
$x_f=x_i+\Delta x$
$x_f=5+2=7m$