Question

Earth is revolving around the sun. If the distance of the earth from the sun is reduced to $1/4th$ of the present distance then the length of present day will be reduced by:

• A. $ \frac{1}{4} $
• B. $ \frac{1}{2} $
• C. $ \frac{1}{8} $
• D. $ \frac{1}{6} $

Answer 1

The Correct Option is C

From Kepler's law
$T^{2} \propto R^{3}$
$\therefore \left(\frac{T_{1}}{T_{2}}\right)^{2} =\left(\frac{R_{1}}{R_{2}}\right)^{3}$
$\frac{T_{1}}{T_{2}} =\left(\frac{R_{1}}{R_{2}}\right)^{3 / 2}=\left(\frac{R}{R / 4}\right)^{3 / 2}$
$=(4)^{3 / 2}=(2)^{3}=8$
$\therefore T_{2} =\frac{T_{1}}{8}$
Hence, the length of the day is reduced by $\frac{1}{8}$.