This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the…
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 energy $_{\text {(rotational) }}$ depends on an angular velocity ' $\omega$ ' and moment of inertia of the body $I$.
i.e., $K \cdot E \cdot\left(\right.$ rotational $=\frac{1}{2} I \omega^2$