Two particles of equal mass are moving with the same linear speed on circular path of radii $r_{1} a n d r_{2}$ . The ratio of centripetal force acting on them will be ___.

\frac{r_{2}}{r_{1}}

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\sqrt{\frac{r_{2}}{r_{1}}}

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{(\frac{r_{1}}{r_{2}})}^{2}

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{(\frac{r_{2}}{r_{1}})}^{2}

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Solution

The correct option is A $\frac{r_{2}}{r_{1}}$
Mass of particle $1 = m_{1}$
Mass of particle $2 = m_{2}$
Linear speed of particle $1 = V_{1}$
Linear speed of particle $2 = V_{2}$
Centripetal force is given by $F = \frac{m v^{2}}{r}$
$∴ \frac{F_{1}}{F_{2}} = \frac{m_{1} V_{1}^{2}}{r_{1}} \times \frac{r_{2}}{m_{2} V_{2}^{2}}$
Since, $m_{1} = m_{2}$ and $V_{1} = V_{2}$
$∴ \frac{F_{1}}{F_{2}} = \frac{r_{2}}{r_{1}}$

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