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This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1$ : When moment of inertia $I$ of a body rotating about an axis with angular speed $\omega $ increases, its angular momentum $L$ is unchanged but the kinetic energy $K$ increases if there is no torque applied on it.
Statement $2$ : $L = I\omega $, kinetic energy of rotation $ = \frac{1}{2}\,I\omega ^2$
Statement $1$ is true, Statement $2$ is true,
Statement $2$ is not the correct explanation of Statement $1$
Statement $1$ is false, Statement $2$ is true.
Statement $1$ is true, Statement $2$ is true,
Statement $2$ is correct explanation of the Statement $1$
Statement $1$ is true, Statement $2$ is false
Solution
AS $L\, = I\omega $ so L increases with increase in $\omega $.
Kinetic $energ{y_{\left( {rotational} \right)}}$ depends on an angular velocity $'\omega '$
and moment of inertia of the body I.
i.e., $K.E{._{\left( {rotational} \right)}} = \frac{1}{2}I{\omega ^2}$
