Explanation

(a) Acceleration of each mass $= a = \left( \frac{m_{1} - m_{2}}{m_{1} + m_{2}} \right)g$
Now acceleration of centre of mass of the system
$A_{cm} = \frac{m_{1}\overrightarrow{a_{1}} + m_{1}\overrightarrow{a_{2}}}{m_{1} + m_{2}}$
As both masses move with same acceleration but in opposite direction so $\overrightarrow{a_{1}} = - \overrightarrow{a_{2}} = a$ (let)
[image:7_image88.png]
$\therefore A_{cm} = \frac{m_{1}a - m_{2}a}{m_{1} + m_{2}}$
$= \left( \frac{m_{1} - m_{2}}{m_{1} + m_{2}} \right) \times \left( \frac{m_{1} - m_{2}}{m_{1} + m_{2}} \right) \times g = \left( \frac{m_{1} - m_{2}}{m_{1} + m_{2}} \right)^{2} \times g$