MHTCET 26 Apr 2025 Shift 2 Paper

Concept:Newton's law of cooling is used with the water equivalent of the calorimeter.Explanation:Let the water equivalent of the calorimeter be $x$ grams.So, the effective thermal mass is $(10 + x)$ grams in the first case and $(20 + x)$ grams in the second case.The average temperature difference with the surroundings is the same in both cases because the temperature falls from $20^{\circ}C$ to $15^{\circ}C$ each time.Thus, the rate of heat loss is proportional to the ratio of effective mass and time.For the first case:$$(10+x) \times \frac{5}{10}$$For the second case:$$(20+x) \times \frac{5}{15}$$Since the surrounding conditions are identical, these two expressions are equal:$$\frac{10+x}{10} = \frac{20+x}{15}$$Cross-multiplying gives:$$15(10+x) = 10(20+x)$$$$150 + 15x = 200 + 10x$$$$15x - 10x = 200 - 150$$$$5x = 50$$$$x = 10$$Answer:The water equivalent of the calorimeter is $10$ g, which corresponds to option C.