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  4. The moment of inertia of a body about a given axis 1.2 kg m 2. Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J and angular acceleration of 25 rad / s 2 must be applied about the axis for a duration of:

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Q. The moment of inertia of a body about a given axis $1.2\, kg \,m ^{2}$. Initially the body is at rest. In order to produce a rotational kinetic energy of $1500\, J$ and angular acceleration of $25\, rad / s ^{2}$ must be applied about the axis for a duration of:

JIPMERJIPMER 2003

Solution:

Kinetic energy is given by
$E =\frac{1}{2} I \omega^{2}, \omega^{2}=\frac{2 E}{I} $
$\omega^{2} =\frac{2 \times 1500}{1.2}=2500 $
$\omega =\sqrt{2500}=50 \,rad / \sec$
$t =\frac{\omega}{\alpha}=\frac{50}{25}=2 \,\sec$