# Moment of inertia of a body about a given axis is $1.5\:kg\:m^{2}$. Initially the body is ate rest. In order to produce a rotational kinetic energy of $1200\:J$ , the angular acceleration of $20\:rad/s^{2}$ must be applied about the axis for a duration of :Option 1)$2.5\:s$Option 2)$2\:s$Option 3)$5\:s$Option 4)$3\:s$

Given

$K.E.= 1200 J$

$\Rightarrow \frac{1}{2}I\:w^{2}=K.E.$

$\Rightarrow w=\sqrt{\frac{2K.E.}{I}}$

$\tau\:t=I\omega$

$\Rightarrow \tau\: t=I \sqrt{ \frac{2K.E.}{I}}$

$\Rightarrow \: t=\frac{I \sqrt{ \frac{2K.E.}{I}}}{I \:\alpha }$

$\Rightarrow \: t= \sqrt{\frac{2K.E.}{I}}\times \frac{1}{\alpha }$

$\Rightarrow \: t= \sqrt{\frac{2\times 1200}{1.5}}\times \frac{1}{20 }=2\:\:seconds$

Option 1)

$2.5\:s$

Option 2)

$2\:s$

Option 3)

$5\:s$

Option 4)

$3\:s$

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