Question

If the distance between the earth and the sun were reduced to half its present value, Then the number of days in one year would have been

• A. 65
• B. 129
• C. 183
• D. 730

Answer 1

The correct option is B

129

$T=\frac{2\pi R}{v}=\frac{2\pi R}{\sqrt{\frac{GM}{R}}}=\frac{2\pi R^{\frac{3}{2}}}{\sqrt{GM}}$

$\Rightarrow \frac{T_2}{T_1}=(\frac{R_2}{R_1}{)}^{\frac{3}{2}}=(\frac{1}{2}{)}^{\frac{3}{2}}=\frac{1}{2\sqrt{2}}$

$\therefore T_2=\frac{365}{2\sqrt{2}}=129day$