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A flywheel whose moment of inertia about its axis of rotation is $16 kg - m^{2}$ is rotating freely in its own plane about a smooth axis through its centre. Its angular velocity is 9 rad $s^{- 1}$ when a torque is applied to bring it to rest in $t_{0}$ seconds. Find $t_{0}$ if
The magnitude of the torque after t seconds is given by k t.

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(1) $11 \sqrt{\frac{2}{k}}$

(2) $12 \sqrt{\frac{2}{k}}$

(3) $64 \sqrt{\frac{2}{k}}$

(4) $22 \sqrt{\frac{2}{k}}$

answer is B.

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Detailed Solution

$\int_{0}^{t_{0}} τdt = Iω ∴ \int_{0}^{t_{0}} ktdt = Iω ∴ \frac{{kt}_{0}^{2}}{2} = Iω ∴ t_{0} = \sqrt{\frac{2 I ω}{k}} = \sqrt{16 \times 9} \sqrt{\frac{2}{k}} = 12 \sqrt{\frac{2}{k}}$

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