Q. Two particles of equal masses are revolving in circular paths of radii $r_{1}$ and $r_{2}$ respectively with the same speed. The ratio of their centripetal forces is
A) $\frac{r_{2}}{r_{1}}$
B) $\sqrt{\frac{r_{2}}{r_{1}}}$
C) $\left( \frac{r_{1}}{r_{2}} \right)^{2}$
D) $\left( \frac{r_{2}}{r_{1}}\ \right)^{2}$
Explanation
(a) $F = \frac{mv^{2}}{r}$. If $\ m$ and $v$ are constants then $F \propto \frac{1}{r}$
$\therefore\frac{F_{1}}{F_{2}} = \left( \frac{r_{2}}{r_{1}} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.