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 $\frac{T_1}{T_2}={\left(\frac{r_1}{x_2}\right)}^{3/2}={\left(\frac{10^{13}}{1012}\right)}^{3/2}$
$=10^{3/2}=10\sqrt{10}$