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 : $T_1=1year,R_1=R,R_2=2R$
According to Kepler's third law of planetary motion
$T^2\propto R^3$
where $R$ is the distance between earth and sun.
$\therefore {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R_1}{R_2}\right)}^3$
$={\left(\frac{R}{2R}\right)}^3=\frac{1}{8}$
$\Rightarrow \frac{T_1}{T_2}=\frac{1}{2\sqrt{2}}$
$\Rightarrow T_2=2\sqrt{2}{T}_1$
$=2\sqrt{2}years$