Question

The distance of two planets from the sun are ${10}^{13}$ m and ${10}^{12}$ m respectively. The ratio of time periods of the planets is

• A. $\sqrt{10}$
• B. $10 \sqrt{10}$
• C. 10
• D. $\frac{1}{\sqrt{10}}$

Answer 1

Answer: (B)

$10 \sqrt{10}$

Answer 2

Distance of two planets from sun $(r_1) = {10}^{13} \,m$ and $(r_2) = {10}^{12} \,m$
Relation between time period (T) and distance of the planet from the sun is $T^2 \propto r^3 \, \, \,$ or $\, \, \, T \propto r^{3/2}$.
Therefore $\frac{ T_1}{T_2} = \bigg( \frac{r_1}{r_2} \bigg)^{3/2} = \bigg( \frac{{10}^{13}}{{10}^{12}} \bigg)^{3/2} = {10}^{3/2} = 10 \sqrt{10}$.