Question

This question has Statement land 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 co 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 $=\frac{1}{2}I{\omega }^2$

• A. Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
• B. Statement 1 is false, Statement 2 is true.
• C. Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation of the Statement 1.
• D. Statement 1 is true, Statement 2 is false.

Answer 1

Answer: (B)

As $L=I\omega$ so L increases with increase in co. Kinetic energy${}_{(rotational)}$ depends on an angular velocity $\omega$ of and moment of inertia of the body I.
$i.e.,K.E{.}_{\left(rotational\right)}=\frac{1}{2}I{\omega }^2$