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Two spheres P and Q each of mass 200 gm are attached to a string of length one metre as shown in figure. The string and the spheres are then whirled in a horizontal circle about ‘O’ at a constant angular speed. The ratio of tension in the string between P and Q to that between P and O is…………(P is the mid point of OQ)

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$\frac{2}{3}$

$\frac{3}{2}$

$\frac{2}{1}$

$\frac{1}{2}$

answer is B.

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Detailed Solution

Here tension in the string is nothing but the centrifugal force. Let 2l be the length of the string. Then Q revolves in A circular path of radius 2l and P in the circular path of radius $l$ .

$∴$ tension in between O and P , $T_{1} = m l ω^{2} + m (2 l) ω^{2} = 3 m l ω^{2}$

Tension in between P and Q $= m (2 l) ω^{2} = 2 m l ω^{2}$

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