MHTCET 23 Apr 2025 Shift 2 Paper

Concept:The potential energy of the falling object is entirely converted into heat energy, which is used to melt ice at $0^\circ C$.Explanation:The object falls from height $h = 2000\ \text{m}$ with mass $m = 3.5\ \text{kg}$.Its potential energy is given by $P.E. = mgh$.This energy is released as heat when the object comes to rest and is used to melt the ice.Step 1: Calculate the potential energy:$$P.E. = 3.5 \times 10 \times 2000 = 70,000\ \text{J}$$Step 2: Let $M$ be the mass of ice melted.The heat required to melt $M$ kg of ice is $Q = M L$, where $L = 3.5 \times 10^5\ \text{J/kg}$.Step 3: Equate the heat released to the heat used for melting:$$M L = mgh$$$$M \times 3.5 \times 10^5 = 70,000$$$$M = \frac{70,000}{3.5 \times 10^5} = 0.2\ \text{kg}$$Converting to grams: $0.2\ \text{kg} = 200\ \text{g}$.Thus, 200 grams of ice melts.Answer:The quantity of ice that melts is $200\ \text{g}$.Correct option: C (200 gram).