Explanation

(a) [image:5_image227.emf]
Here, $m_{1} = 1kg,\ m_{2} = 2kg$
The acceleration of the system is
$a = \frac{\left( m_{2} - m_{1} \right)g}{m_{1} + m_{2}} = \frac{(2 - 1)g}{1 + 2} = \frac{g}{3} = \frac{10}{3}$
Acceleration of the centre of mass is
$a_{cm} = \frac{m_{1}a_{1} + m_{2}a_{2}}{m_{1} + m_{2}} = \frac{1( - a) + 2(a)}{1 + 2} = \frac{1\left( \frac{- g}{3} \right) + 2\left( \frac{g}{3} \right)}{3}$
$= \frac{g}{9} = \frac{10}{9}$
The distance travelled by the centre of mass in two seconds is
$S = \frac{1}{2}a_{cm}t^{2} = \frac{1}{2} \times \frac{10}{9} \times (2)^{2} = \frac{20}{9}m$