Question

Hailstone at $0^{\circ}C $ falls from a height of $1\, km$ on an insulating surface converting whole of its kinetic energy into heat. What part of it will melt? $ (g=10\,m/s^{2})$ (Latent heat of ice $ =3.34\times 10^{5}J/kg$)

• A. $ \frac{1}{33} $
• B. $ \frac{1}{18} $
• C. $ \frac{3}{3}\times 10^{-4}$
• D. All of it will melt

Answer 1

Answer: (A)

Hailstone possesses potential energy due to its height.
Let $k$ be the fraction of ice that melts.
Hence. potential energy $=k \times$ latent heat $mgh=kmL$
$\Rightarrow k=\frac{g h}{L}=\frac{10 \times 1000}{3.34 \times 10^{5}} \approx \frac{1}{33}$