Question

# A piece of ice falls from a height h so that $\mathrm{t}$ melts completely. Only one-quarter of the heat produced is absorbed $\mathrm{b}$ the ice, and all energy of ice gets converted into heat during its fall. The value of $\mathrm{h}$ is? (Latent heat of force is $3.4×{10}^{5}\mathrm{J}/\mathrm{k}$ and $\mathrm{g}=10\mathrm{N}/\mathrm{kg}$).

A

$34\mathrm{km}$

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B

$68\mathrm{km}$

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C

$136\mathrm{km}$

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D

$544\mathrm{km}$

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Solution

## The correct option is C $136\mathrm{km}$Step 1. Given dataA piece of ice falls from a height h so that $\mathrm{t}$ melts completely. Only one-quarter of the heat produced is absorbed $\mathrm{b}$ the ice, and all energy of ice gets converted into heat during its fall.Latent heat of ice $=3.4×{10}^{5}\mathrm{J}/\mathrm{k}$$\mathrm{g}=10\mathrm{N}/\mathrm{kg}$We have to find the value of $\mathrm{h}$.Step 2. Concept to be usedIn physics, the conservation of energy is the total energy of an isolated system remains constant irrespective of whatever internal changes may take place with energy disappearing in one form reappearing in another.According to conservation of energy, energy obtained by the ice during its fall from height $\mathrm{h}$ is given by,$\mathrm{E}=\mathrm{mgh}$Here, $\mathrm{E}$ is the potential energy, $\mathrm{m}$ is the mass of object, $\mathrm{g}$ is gravity and $\mathrm{h}$ is height.Step 3: Find the value of height.It is given that, only one- quarter of its energy is absorbed by the ice.Therefore, $\frac{\mathrm{mgh}}{4}={\mathrm{mL}}_{\mathrm{f}}$Here, ${\mathrm{L}}_{\mathrm{f}}$ is latent heat of force.Put the all given value in the above equation. We get, $\mathrm{h}=\frac{{\mathrm{mL}}_{\mathrm{f}}×4}{\mathrm{mg}}$$=\frac{3.4×{10}^{5}×4}{10}$$=13.6×{10}^{4}$$=13600\mathrm{m}$$=136\mathrm{km}$So, the value of $\mathrm{h}$ is $136\mathrm{km}$.Hence, option $\mathrm{C}$ is the correct answer.

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