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Q.

The moment of inertia of a body about an axis is 1.2 kg-m². Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/s² must be applied about the axis for a duration of (in seconds)

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Detailed Solution

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$E = \frac{1}{2} {Iω}^{2}$

$\Rightarrow ω = \sqrt{\frac{2 E}{I}} = \sqrt{\frac{2 \times 1500}{1.2}} = 50 rad / s$

Time taken to attain this value of $ω$ is $t = \frac{ω - 0}{α} = \frac{50}{25} = 2 s$

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