There are two lead spheres at the same temperature, the ratio of radii being 1 : 2. The ratio of heat capacities are:

1 : 2

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1: 4

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1 : 6

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1 : 8

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Solution

The correct option is D 1 : 8
$\frac{R_{1}}{R_{2}} = \frac{1}{2}, d_{1} = d_{2}, S_{1} = S_{2}$
(as they are of same material)
$\frac{C_{1}}{C_{2}} = \frac{m_{1} S_{1}}{m_{2} S_{2}} = \frac{d_{1} V_{1}}{d_{2} V_{2}} \frac{S_{1}}{S_{2}}$

$\Rightarrow \frac{V_{1}}{V_{2}} = \frac{R_{1}^{3}}{R_{2}^{3}} = \frac{1^{3}}{2^{3}}$
$∴ C_{1} : C_{2} = 1 : 8$

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There are two lead spheres at the same temperature, the ratio of radii being 1 : 2. The ratio of heat capacities are:

The correct option is D 1 : 8R1R2=12,d1=d2,S1=S2(as they are of same material)C1C2=m1S1m2S2=d1V1d2V2S1S2⇒V1V2=R31R32=1323∴C1:C2=1:8