Two particles of equal masses are revolving in circular paths of radii $r_{1}$ and $r_{2}$ respectively with the same period.The ratio of their centripetal force is

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

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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 $\frac{r_{1}}{r_{2}}$
$F_{1} = m r_{1} ω^{2}, F_{2} = m r_{2} ω^{2}$
Since, period, $T$ , is same , so $ω$ is same , because $T = \frac{2 π}{ω}$
Hence, $\frac{F_{1}}{F_{2}} = \frac{r_{1}}{r_{2}}$

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Two particles of equal masses are revolving in circular paths of radii r1 and r2 respectively with the same period.The ratio of their centripetal force is

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Two particles of equal masses are revolving in circular paths of radii $r_{1}$ and $r_{2}$ respectively with the same period.The ratio of their centripetal force is

The correct option is A $\frac{r_{1}}{r_{2}}$
$F_{1} = m r_{1} ω^{2}, F_{2} = m r_{2} ω^{2}$
Since, period, $T$ , is same , so $ω$ is same , because $T = \frac{2 π}{ω}$
Hence, $\frac{F_{1}}{F_{2}} = \frac{r_{1}}{r_{2}}$