Question

A nail at $0^{o}C$ falls from a height of 1 km on an ice surface and its whole kinetic energy is converted into heat. What fraction of it will melt?

• A. $\frac{1}{33}$
• B. $\frac{1}{8}$
• C. $\frac{1}{33}\times {10}^{-4}$
• D. whole of it will melt

Answer 1

The correct option is A $\frac{1}{33}$

Let mass of nail = $m_{nail}$
mass of ice that melts = $m_{ice}$
The nail falls from a height of 1 km.
The potential energy $=mgh=mg\left({10}^3\right)J$
When the nail falls, all of this potential energy gets converted into kinetic and thus into heat.
This heat energy melts $m_{ice}$ mass of ice i.e.
$m_{nail}g\left({10}^3\right)J=m_{ice}L$ where L is the latent heat of fusion of ice $=333.55KJ/kg$
$\frac{m_{ice}}{m_{nail}}=\frac{g\times {10}^3}{L}=\frac{1}{33}$