Question

The earth revolves around the sun in one year. If distance between them becomes double, the new time period of revolution will be

• A. $4 \sqrt 2 $ years
• B. $2 \sqrt 2 $ years
• C. 4 years
• D. 8 years

Answer 1

Answer: (B)

Given : $T_1 = 1\, year, R_1 = R, R_2 = 2R $
According to Kepler's third law of planetary motion
$T^2 \propto R^3$
where $R$ is the distance between earth and sun.
$\therefore \left(\frac{T_1}{T_2}\right)^2 = \left(\frac{R_1}{R_2}\right)^3 $
$ = \left(\frac{R}{2R}\right)^3 = \frac{1}{8}$
$\Rightarrow \frac{T_1}{T_2} = \frac{1}{2 \sqrt 2}$
$\Rightarrow T_2 = 2 \sqrt 2 T_1 $
$= 2 \sqrt 2 \, years$