Question

The time of revolution of planet $A$ around the sun is 8 times that of another planet $B$. The distance of planet $A$ from the sun is how many times greater than that of the planet $B$ from the sun?

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (C)

4

Time period $T^2=\frac{4{\pi }^2}{GM}{R}^3$
i.e $T^2\propto R^3$
$\Rightarrow {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R_1}{R_2}\right)}^3$
$\Rightarrow 8^2={\left(\frac{R_1}{R_2}\right)}^3$
$\Rightarrow \frac{R_1}{R_2}=8^{2/3}=4$