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Three point masses each of mass ‘ $m$ ’ are joined together using a string to form an equilateral triangle of side ‘ $a$ ’. The system is placed on a smooth horizontal surface and rotated with a constant angular velocity ‘ $ω$ ’ about a vertical axis passing through the centroid. Then the tension in each string is

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${\frac{ma ω}{3}}^{2}$

$3 ma ω^{2}$

$ma ω^{2}$

$\frac{ma ω^{2}}{\sqrt{3}}$

answer is C.

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Detailed Solution

$\cos 30^{\circ} = \frac{a / 2}{r} \Rightarrow r = \frac{a}{\sqrt{3}}$

$2 Tcos 30^{\circ} = mr ω^{2}$

$\sqrt{3} T = m \frac{a}{\sqrt{3}} ω^{2}$

$T = \frac{ma ω^{2}}{3}$

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