`A` lead ball at `30^(@)C` is dropped from a height h. The ball is heated due to the air resistance and it completely melts just before reaching the ground, The molten substance falls slowly on the ground. Latent heat of fusion of lead is `22200 Jk//g` . Specific heat capacity of lead `=126J//kg-^(@)C` and melting point of lead `=330^(@)C`, Assume that all mechanical energy lost is used to heat the ball.
Find the value of h in km ? `("Use" g=10 m//s2)`

Explanation

All this energy is used to heat the ball as it reaches the ground with a small velocity. Energy required to take the ball from `30^(@)Cto 300^(@)C` is
`mxx(126 J//kg-^(@)C)xx(300^(@)C)`
`=mxx37800 J//kg` and
energy required to melt the ball at `330^(@)C=mL` where `L=` latent heat of fusion of lead
Thus, `mxxgh=mxx37800 J//kg+m22200` or, `h=6km`
So, Answer is `6`