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A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is [Latent heat of ice is $3.4 \times 10^{5}$ J/kg and g = 10 N/kg]
A
544 km
B
136 km
C
68 km
D
34 km
Explanation
$mgh/4 = mL$.
Detailed Solution
Potential energy of ice at height h = mgh; heat absorbed by the ice $= \frac{mgh}{4}$
Energy required to melt the ice = mL
$\frac{mgh}{4} = mL \Rightarrow h = \frac{4L}{g} = \frac{4\times3.4\times10^{5}}{10}$ m
$h = 136\times10^{3}$ m = 136 km
Energy required to melt the ice = mL
$\frac{mgh}{4} = mL \Rightarrow h = \frac{4L}{g} = \frac{4\times3.4\times10^{5}}{10}$ m
$h = 136\times10^{3}$ m = 136 km