If the earth is at one-fourth of its prese

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If the earth is at one-fourth of its present distance from the sun, the duration of the year will be

A

Half the present year

B

One-eighth the present year

C

One-fourth the present year

D

One-sixth the present year

If the earth is at one-fourth of its present distance from the sun, the duration of the year will be

Since ${T^2} \propto {r^3}$

$\therefore \,\,{\left( {\frac{{T'}}{T}} \right)^2} = {\left( {\frac{1}{4}} \right)^3}\,$

$\Rightarrow \,T' = \frac{1}{8}T$