Q. According to Kelper’s law of planetary motion if $T$ represent time period and $r$ is orbital radius, then for two planets these are related as
A) $\left( \frac{T_{1}}{T_{2}} \right)^{3} = \left( \frac{r_{1}}{r_{2}} \right)^{3}$
B) $\left( \frac{T_{1}}{T_{2}} \right)^{\frac{3}{2}} = \frac{r_{1}}{r_{2}}$
C) $\left( \frac{T_{1}}{T_{2}} \right)^{4} = \left( \frac{r_{1}}{r_{2}} \right)^{3}$
D) $\left( \frac{T_{1}}{T_{2}} \right)^{2} = \left( \frac{r_{1}}{r_{2}} \right)^{3}$
Explanation
(d) According to Kepler’s law $T^{2} \propto r^{3}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left( \frac{T_{1}}{T_{2}} \right)^{2} = \ \left( \frac{r_{1}}{r_{2}} \right)^{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.