Question

A rigid body of mass $m$ rotates about an axis passing through its center. If the angular velocity of body is unity, the moment of inertia of the body will be equal to :
a. Kinetic energy of the body.
b. Twice the kinetic energy of the body.
c. Angular momentum of the body.
d. Twice the angular momentum of the body.

Answer 1

Hint: The formula of kinetic energy of a rotational body is given by the formula,
$K.E. = \dfrac{1}{2}I{\omega ^2}$
where $I$= moment of inertia of body
            $\omega $= angular velocity of body

Step by step solution:
According to question,
Angular velocity of the body, $\omega $= 1

Kinetic energy of a rotating body, $K.E. = \dfrac{1}{2}I{\omega ^2}$

On substituting the value of $\omega $=1 in the above formula of kinetic energy we get,
$K.E. = \dfrac{1}{2}I{(1)^2}$

$K.E. = \dfrac{1}{2}I$$ \Leftrightarrow I = 2K.E.$

Hence the moment of inertia ($I$) becomes two times the kinetic energy of the body. b
Therefore the correct option is B.

Note: The given formula of kinetic energy is only valid for rigid bodies because the distance of all the particles during rotation remains constant hence the angular velocity of all the particles contributing to the body remains uniform throughout the rotatory motion.