A rigid body of mass $m$ rotates about an axis passing through its centre. If the angular velocity of the body is unity, the moment of inertia of the body will be equal to :

Kinetic energy of the body

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Twice the kinetic energy of the body

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Angular momentum of the body

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Twice the angular momentum of the body

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Solution

The correct option is A Twice the kinetic energy of the body
Rotatory kinetic energy, $K_{R} = \frac{1}{2} I ω^{2}$
According to question
$ω = 1$
$∴ K = \frac{1}{2} I \times (1)^{2}$
$K = \frac{1}{2} I$
or $2 K = I$
Therefore, the moment of inertia of the body will equal to twice the kinetic energy of the body.

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