Q. Two bodies of mass $10\ kg$ and $5\ kg$ moving in concentric orbits of radii $R$ and $r$ such that their periods are the same. Then the ratio between their centripetal acceleration is
A) $R/r$
B) $r/R$
C) $R^{2}/r^{2}$
D) $r^{2}/R^{2}$
Explanation
(a) $\frac{a_{R}}{a_{r}} = \frac{\omega_{R \times R}^{2}}{\omega_{r}^{2} \times r} = \frac{T_{r}^{2}}{T_{R}^{2}} \times \frac{R}{r} = \frac{R}{r}\lbrack As\ T_{r} = T_{R}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.