Question

A block of ice with mass $m$ falls into a lake. After impact, a mass of ice $\frac{m}{5}$ melts. Both the block of ice and the lake have a temperature of $0^o$. If $L$ represents the heat of fusion, the minimum distance the ice fell before striking the surface is

• A. $\frac{L}{5g}$
• B. $\frac{5L}{g}$
• C. $\frac{gL}{5m}$
• D. $\frac{ml}{5g}$

Answer 1

The correct option is A $\frac{L}{5g}$

Let the height from where the ice block falls to the lake is $h$.
Change in potential energy $PE=mgh$

where $g$ is the acceleration due to gravity.
The PE loss on reaching the lake is converted to KE of the ice block and is converted into heat on impact.
Amount of heat required to melt mass of $\frac{m}{5}$ is $\frac{m}{5}L$

where L is the latent heat of fusion.
Equating both, we get
$mgh=\frac{m}{5}L$
$\therefore h=\frac{L}{5g}$