Explanation

(a) Acceleration of combined system,
$a = \frac{m_{1} - m_{2}}{m_{1} + m_{2}}.g$
$= \frac{3 - 2}{3 + 2} \times 9.8 = 1.96\ ms^{- 2}$
Vertically upward velocity of 2 kg mass at the time breaking of string,
$v = at = 5 \times 1.96 = 9.8\ ms^{- 2}$
After breaking of string, mass $m_{2}$ moves under gravity and go further higher through a height $h$, where final velocity is zero. Hence
$(0)^{2} - (9.8)^{2} = 2 \times ( - 9.8) \times h$ or $h = 4.9\ $m