1. Tardigrade
  2. Question
  3. Physics
  4. Two objects A and B of weight 10 kg and 20 kg respectively are kept at two points on the x-axis. B is moved 9 cm along the x-axis. By what distance A should be moved to keep the centre of mass the same?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Two objects $A$ and $B$ of weight 10 kg and 20 kg respectively are kept at two points on the $x$-axis. B is moved 9 cm along the $x$-axis. By what distance A should be moved to keep the centre of mass the same?

JIPMERJIPMER 2016System of Particles and Rotational Motion

Solution:

To keep centre of mass at same point
$r_{CM}\left(before\right) = r_{CM}\left(Final\right)$
$\frac{m_{1}r_{1}+m_{2}r_{2}}{m_{1}+m_{2}}=\frac{m_{1}\left(r_{1}+x\right)+m_{2}\left(r_{2}+9\right)}{m_{1}+m_{2}}$
$m_{1}r_{1}+m_{2}r_{2}=m_{1}r_{1}+m_{1}x_{1}+m_{2}r_{2}+9m_{2} m_{1}x=-9m_{2}$
$ x=\frac{9m_{2}}{m_{1}}$ [neglecting negative sign]
$ x=9 \times\frac{20}{10}=18 cm$