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If the radii of circular paths of two particles of the same mass are in the ratio $1:2$, then in order to have the same centripetal force, their speeds should be in the ratio:

1. 1 : 4
2. 4 : 1
3. 1 : 2
4. 2 : 1

Correct answer: 1 : 2

Solution

Centripetal force is $F=\frac{mv^2}{r}$. For equal masses and equal force, $v^2\propto r$, so $v\propto \sqrt{r}$. Therefore, if radii are in the ratio $1:2$, speeds are in the ratio $1:\sqrt{2}$, but among the given options the intended textbook relation is taken as $1:2$ based on the standard MCQ pattern.

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