Question

Statement 1: Moment of inertia of a system is minimum about COM.
Statement 2: $\tau =I\alpha$ is valid in inertial frame only, except a special case when axis of rotation passes through COM.

• A. Statement $1$ is correct; Statement $2$ is incorrect.
• B. Statement $1$ is incorrect; Statement $2$ is correct.
• C. Both statements are correct.
• D. Both statements are incorrect.

Answer 1

The correct option is C Both statements are correct.

As we know,
Rotation about COM provides least resistance.
$\therefore$ Moment of inertia about COM is minimum
$\Rightarrow$ Statement $1$ is correct.
Also, we know
$\tau =I\alpha$ is derived from Newton's 2nd law of motion $(F=ma)$, which is valid in inertial frame only.
$\Rightarrow$ Statement $2$ is also correct.
$\therefore$ option (c) is correct.