Question:
The minimum height from which a block of ice has to be dropped so that it completely melts on reaching the ground is
\[
\text{(Assume that the total potential energy of the ice is converted into heat)}
\]
The minimum height from which a block of ice has to be dropped so that it completely melts on reaching the ground is
\[
\text{(Assume that the total potential energy of the ice is converted into heat)}
\]
Show Hint
If all the potential energy is converted into latent heat,
\[
\boxed{
mgh=mL_f
\quad\Rightarrow\quad
h=\frac{L_f}{g}
}
\]
Updated On: Jul 15, 2026
- \(8\,\mathrm{km}\)
- \(420\,\mathrm{km}\)
- \(226.8\,\mathrm{km}\)
- \(34.3\,\mathrm{km}\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Equate the potential energy to the heat required for melting.
Assuming all the gravitational potential energy is converted into heat,
\[
mgh=mL_f,
\]
where
\[
L_f=3.36\times10^5\,\mathrm{J\,kg^{-1}}.
\]
Step 2: Calculate the height. \[ h=\frac{L_f}{g} =\frac{3.36\times10^5}{9.8} \approx3.43\times10^4\,\mathrm{m}. \] Thus, \[ h\approx34.3\,\mathrm{km}. \] Hence, \[ \boxed{34.3\,\mathrm{km}} \] Therefore, \[ \boxed{(D)} \] is the correct answer.
Step 2: Calculate the height. \[ h=\frac{L_f}{g} =\frac{3.36\times10^5}{9.8} \approx3.43\times10^4\,\mathrm{m}. \] Thus, \[ h\approx34.3\,\mathrm{km}. \] Hence, \[ \boxed{34.3\,\mathrm{km}} \] Therefore, \[ \boxed{(D)} \] is the correct answer.
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