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A circular disc is rotating about its own axis at a uniform angular velocity 'ω '. The disc is subjected to uniform angular retardation by which its angular velocity is decreased to ω/2 during 120 rotations. The number of rotations further made by it before coming to rest is

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120

answer is C.

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Detailed Solution

as $α$ constant
$α = \frac{ω^{2} - {ω_{0}}^{2}}{2 θ} = \frac{ω^{2} - {ω_{0}}^{2}}{2 (2 πN)}$

$∴ N \propto ω^{2} - {ω_{0}}^{2}$

$\frac{N}{N^{'}} = \frac{{(\frac{ω}{2})}^{2} - ω^{2}}{0 - {(\frac{ω}{2})}^{2}} = \frac{\frac{- 3}{4}}{\frac{- 1}{4}} = 3$

$∴ N^{'} = \frac{N}{3} = \frac{120}{3} = 40$

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