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)

Distance of two planets from sun $\left(r_{1}\right)=10^{13} m$ and $\left(r_{2}\right)=10^{12} m$.
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 $\frac{T_{1}}{T_{2}}=\left(\frac{r_{1}}{x_{2}}\right)^{3 / 2}=\left(\frac{10^{13}}{1012}\right)^{3 / 2}$
$=10^{3 / 2}=10 \sqrt{10}$