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

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$1 : 3$

$3 : 4$

$3 : 1$

$4 : 3$

answer is B.

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Detailed Solution

$\frac{m_{1}}{m_{2}} = \frac{2}{3}; \frac{S_{1}}{S_{2}} = \frac{2}{3}; \frac{θ_{1}}{θ_{2}} = \frac{1}{2};$

$\frac{m_{1} {gh}_{1}}{m_{2} {gh}_{2}} = \frac{{Jm}_{1} S_{1} {Δθ}_{1}}{{Jm}_{2} S_{2} {Δθ}_{2}} \Rightarrow \frac{h_{1}}{h_{2}} = \frac{2}{3} \cdot \frac{1}{2} = \frac{1}{3}$

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