A ball is dropped from a height of 1000 Km .Due to heat from air friction & melts just before reaching the ground . The latent heat of fusion of ball's material is - (specific heat of material =100 $\;{J kg^{-1}}^{0}C$ Air tempeature=$\;25^{0}C\;$ , Melting point =$\;{J kg^{-1}}^{0}C\;$)

Question

$(a)\;9.1\;MJkg^{-1}\qquad(b)\;9.3\;MJkg\qquad(c)\;9.7\;MJkg^{-1}\qquad(d)\;None\;of\;these$

Answer 1

Answer : (c) $\;9.7\;MJkg^{-1}$

Explanation :

Initial energy of ball = $\;mgh=m \times 9.8 \times 1000 \times 10^{3}$

$=9.8 m \times 10^{6} J$

This energy heats up the ball to $\;1125^{0}C\;$ & meets it

$9.8 \times 10^{6}=m \times 100 \times (1125-25)+m \times L$

$9.8 \times 10^{6}=100 \times 1100 +mL$

$9.8 \times 10^{6}=0.11\times10^{6}+L$

$L=9.69 \times 10^{6} J kg^{-1}\;.$