Q. The period of revolution of planet $A$ around the sun is 8 times that $B$. The distance of a from the sun is how many times greater than that of $B$ from the sun?
A) 2
B) 3
C) 4
D) 5
Explanation
(b) As $T^{2} \propto r^{3}$,
so, $\frac{T_{A}^{2}}{T_{B}^{2}} = \frac{r_{A}^{3}}{r_{B}^{3}}$
or $\frac{r_{A}}{r_{B}} = \left( \frac{T_{A}}{T_{B}} \right)^{2/3} = (8)^{2/3} = 4$
or $r_{A} = 4r_{B};$
so $r_{A} - r_{B} = 4r_{B} - r_{B} = 3r_{B}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.