Two stones of masses and are whirled in horizontal circles, the heavier one in a radius and the lighter one in radius . The tangential speed of lighter stone is times that of the value of heavier stone when they experience same centripetal forces. The

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Solution

Q.
Two stones of masses $m$ and $2 m$ are whirled in horizontal circles, the heavier one in a radius $r / 2$ and the lighter one in radius $r$ . The tangential speed of lighter stone is $n$ times that of the value of heavier stone when they experience same centripetal forces. The value of $n$ is [2015]

1 4

2 1

3 2

4 3

Ans.
(3)

Let $v$ be tangential speed of heavier stone. Then, centripetal force experienced by lighter stone is

   ${(F_{c})}_{lighter} = \frac{m {(n v)}^{2}}{r}$

and that of heavier stone is ${(F_{c})}_{heavier} = \frac{2 m v^{2}}{(r / 2)}$

But ${(F_{c})}_{lighter} = {(F_{c})}_{heavier}$ (given)

$∴$    $\frac{m {(n v)}^{2}}{r} = \frac{2 m v^{2}}{(r / 2)} or, n^{2} (\frac{m v^{2}}{r}) = 4 (\frac{m v^{2}}{r})$

   $n^{2} = 4 or n = 2$

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