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Physics Question on thermal properties of matter

Hailstone at 0∘C0^{\circ}C falls from a height of 1 km1\, km on an insulating surface converting whole of its kinetic energy into heat. What part of it will melt? (g=10 m/s2) (g=10\,m/s^{2}) (Latent heat of ice =3.34×105J/kg =3.34\times 10^{5}J/kg)

A

133\frac{1}{33}

B

118\frac{1}{18}

C

33×10−4 \frac{3}{3}\times 10^{-4}

D

All of it will melt

Answer

133\frac{1}{33}

Explanation

Solution

The correct option is(A): 133\frac{1}{33}.

Hailstone possesses potential energy due to its height.
Let kk be the fraction of ice that melts.
Hence. potential energy =k×=k \times latent heat mgh=kmLmgh=kmL
⇒k=ghL=10×10003.34×105≈133\Rightarrow k=\frac{g h}{L}=\frac{10 \times 1000}{3.34 \times 10^{5}} \approx \frac{1}{33}