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Q.

Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in the 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

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a

2

b

1

c

3

d

4

answer is B.

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Detailed Solution

$\begin{array}{l} F_{H} = \frac{2 {mv}^{2}}{r / 2} = 4 \frac{{mv}^{2}}{r} \\ F_{l} = \frac{{mv}_{1}^{2}}{r} & v_{1} = nv \Rightarrow F_{1} = \frac{{mn}^{2} v^{2}}{r} \\ F_{1} = F_{H} \Rightarrow \frac{4 {mv}^{2}}{r} = \frac{{mn}^{2} v^{2}}{r} \\ n^{2} = 4 \Rightarrow n = 2 \end{array}$

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