Two particles of equal mass are revolving in circular path of radii $5 m$ and $10 m$ respectively, with the same speed. The ratio of the centripetal force acting on each particle is

1

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2

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0.25

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4

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Solution

The correct option is B $2$
Given, $m_{1} = m_{2} = m$ (say)
$v_{1} = v_{2} = v$ (say)
$r_{1} = 5 m$
$r_{2} = 10 m$
Centripetal force of particle 1 $(F_{1}) = \frac{m_{1} v_{1}^{2}}{r_{1}}$
Centripetal force of particle 2 $(F_{2}) = \frac{m_{2} v_{2}^{2}}{r_{2}}$
Then, $\frac{F_{1}}{F_{2}} = \frac{m_{1}}{m_{2}} \times \frac{r_{2}}{r_{1}} \times \frac{v_{1}^{2}}{v_{2}^{2}}$ ,
as $(m_{1} = m_{2})$ and $(v_{1} = v_{2})$

$\frac{F_{1}}{F_{2}} = \frac{r_{2}}{r_{1}} = \frac{10}{5} = 2$

Hence option B is the correct answer

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Two particles of equal mass are revolving in circular path of radii 5 m and 10 m respectively, with the same speed. The ratio of the centripetal force acting on each particle is

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