Q125 / 150 · MHT CET 2025 (23 Apr Shift 2) · Physics

A stationary object at $4^{\circ} \mathrm{C}$ and weighing 3.5 kg falls from a height of 2000 m on snow mountain at $0^{\circ} \mathrm{C}$. If the temperature of the object just before hitting the snow is $0^{\circ} \mathrm{C}$ and the object comes to rest immediately then the quantity of ice that melts is (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$, Latent heat of ice $\left.=3.5 \times 10^5 \mathrm{~J} / \mathrm{kg}\right)$

  • A
    2 gram
  • B
    20 gram
  • Correct answer
    C
    200 gram
  • D
    2 kg

Solution

The object's gravitational potential energy at height $h$ is converted entirely into heat upon impact. Using $g = 10\mathrm{m\cdot s^{-2}}$, the energy released is $mgh = (3.5)(10)(2000) = 70,000\mathrm{J}$.

This heat melts a mass $m$ of ice at $0^\circ\mathrm{C}$, satisfying $mL_f = 70,000$, where $L_f = 3.5 \times 10^5\mathrm{J\cdot kg^{-1}}$. Solving gives $m = \frac{70,000}{3.5 \times 10^5} = \frac{2}{10} = 0.2\mathrm{kg}$.

The mass melted is $0.2 \times 1000 = 200\mathrm{g}$.

The quantity of ice melted is $200\mathrm{g}$.

Hence, the correct answer is option: 'C'.

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