Question

The radii of circular paths of two particles of same mass are in ratio 6 : 8 then what will be velocities ratio if they have a constant centripetal force?

• A. $\sqrt{3}: 4$
• B. $ 4 : \sqrt{3}$
• C. $ 2 : \sqrt{3}$
• D. $ \sqrt{3}: 2$

Answer 1

Answer: (D)

Here, $\frac{r_{1}}{r_{2}}=\frac{6}{8}, \frac{m_{1}}{m_{2}}=1$
$\frac{F_{1}}{F_{2}}=1\quad$ or, $\quad F_{1}=F_{2}$
or $\frac{m_{1}v^{2}_{1}}{r_{1}}=\frac{m_{2}v^{2}_{2}}{r^{2}}$
or $\frac{v^{2}_{1}}{v^{2}_{2}}=\frac{r_{1}}{r_{2}}\times\frac{m_{2}}{m_{1}}=\frac{6}{8}\times1=\frac{3}{4}$
$\therefore \frac{v_{1}}{v_{2}}=\frac{\sqrt{3}}{2}$