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(D) According to the Stefan-Boltzmann law,the total power radiated by a spherical body of radius $R$ and temperature $T$ is given by $P = \sigma (4\pi

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$64$

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(D) According to the Stefan-Boltzmann law,the total power radiated by a spherical body of radius $R$ and temperature $T$ is given by $P = \sigma (4\pi R^2) T^4$.Since the radiant energy $Q$ received on Earth is proportional to the power radiated by the sun,we have $Q \propto R^2 T^4$.Let the initial energy be $Q_1 = k R^2 T^4$ and the final energy be $Q_2 = k (2R)^2 (2T)^4$.Taking the ratio,we get $\frac{Q_2}{Q_1} = \left( \frac{2R}{R} ight)^2 	imes \left( \frac{2T}{T} ight)^4$.$\frac{Q_2}{Q_1} = (2)^2 	imes (2)^4 = 4 	imes 16 = 64$.Therefore,the ratio of the radiant energy received on the earth is $64$.

If the temperature of the sun were to be increased from $T$ to $2T$ and its radius from $R$ to $2R$,then the ratio of the radiant energy received on the earth to what it was previously will be

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