Two spheres A and B with masses in the ratio 2 : 3 and specific heat 2 : 3 fall freely from rest. If the rise in their temperatures on reaching the ground are in the ratio 1 : 2 the ratio of their heights of fall is

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3 : 1

3 : 4

1 : 3

4 : 3

answer is B.

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Detailed Solution

$\begin{array}{l} m_{A} : m_{B} = 2 : 3; s_{A} : s_{B} = 2 : 3 \\ {Δθ}_{A} : {Δθ}_{B} = 1 : 2; \\ mgh = JmsΔθ; \\ h \propto sΔθ \\ \frac{h_{A}}{h_{B}} = \frac{s_{A}}{s_{B}} \times \frac{{Δθ}_{A}}{{Δθ}_{B}} = \frac{2}{3} \times \frac{1}{2} = 1 : 3 \end{array}$

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