Question

An ice block at ${{0}^{\circ }}C$ is dropped from height h above the ground. What should be the value of h so that it just melts completely by the time it reaches the bottom assuming the loss of whole gravitational potential energy is used as heat by the ice?[ Given: ${{L}_{f}}=80cal/gm$ ]
(A) 33.6m
(B) 33.6km
(C ) 8m
(D) 8km

Answer 1

Hint: Since here the ice block is dropped from a height, the energy associated here is the potential energy. The height at which the ice completely melts is calculated by assuming that the gravitational potential energy is equal to the amount of heat produced by the ice. Hence, by equating the both equation and substituting the values we will get the height where the ice completely melts. Here the principle of conservation of energy is employed here. That is, the total mechanical energy of a system is always conserved if the forces doing work are conservative. If some of the forces are non-conservative, it may get transformed into other forms of energy such as heat, light and sound.

Complete answer:
Applying energy conservation,
$mgh=m{{L}_{f}}$
$\Rightarrow h=\dfrac{{{L}_{f}}}{g}$
Substituting the values we get,
$\begin{align}
  & h=\dfrac{80\times 4.2\times 1000}{10} \\
 & \Rightarrow h=\dfrac{336\times {{10}^{3}}}{10} \\
 & \therefore h=33.6km \\
\end{align}$

Hence, option (B) is correct.

Note:
The term potential energy means the stored energy. Here the principle of conservation of energy is employed here. That is, the total mechanical energy of a system is always conserved if the forces doing work are conservative. If some of the forces are non-conservative, it may get transformed into other forms of energy such as heat, light and sound. However, the total energy of an isolated system always remains the same. Energy can be transformed from one form to another but the total energy of an isolated system always remains constant. Energy can neither be created nor destroyed. That is, the total energy of the universe is a constant. If one part loses energy, another part just gains an equal amount of energy.