If the radii of circular paths of two particles of same masses are in the ratio of 1:2, then in order to have a constant centripetal force, their velocities should be in the ratio of

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$1 : \sqrt{2}$

$4 : 1$

$1 : 4$

$\sqrt{2} : 1$

answer is C.

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Detailed Solution

Given that

$m_{1} = m_{2}, r_{1} : r_{2} = 1 : 2$

In order to have constant centripetal force

$F_{1} = F_{2}, V_{1} : V_{2} = ?$

We know

$F = \frac{{mv}^{2}}{r}$

We need

$\frac{v^{2}}{r} = const$

$∴ \frac{V_{1}}{V_{2}} = \sqrt{\frac{r_{1}}{r_{2}}} = \sqrt{\frac{1}{2}}$

$∴ V_{1} : V_{2} = 1 : \sqrt{2}$

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