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  4. A mass m rotating freely in a horizontal circle of radius 1m on a frictionless smooth table supports a stationary mass 2m , attached to the other end of the string passing through a smooth hole O in table, hanging vertically. Find the angular velocity of rotation. <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-458x0eypjla0dixq.jpg />

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Q. A mass $m$ rotating freely in a horizontal circle of radius $1m$ on a frictionless smooth table supports a stationary mass $2m$ , attached to the other end of the string passing through a smooth hole $O$ in table, hanging vertically. Find the angular velocity of rotation.
Question

NTA AbhyasNTA Abhyas 2022

Solution:

Tension in string balances gravity of mass $2m$ and provide centripetal acceleration to mass $m$ .
$T=2mg=mr\omega ^{2}$
$\Rightarrow \omega =\sqrt{\frac{2 g}{r}}=\sqrt{2 g}rads^{- 1}$