Question

Statement - $\text{I}$: $\overrightarrow{L}=I\overrightarrow{\omega }$ is always true for bodies of all shapes.
Statement- $\text{II}$: $\overrightarrow{\tau }=\frac{d\overrightarrow{L}}{dt}$ is always true in inertial frames.

• A. Statement $\text{I}$ is true, statement $\text{II}$ is true and statement$\text{II}$ is correct explanation for statement $\text{I}$
• B. Statement $\text{I}$ is true, statement $\text{II}$ is true but statement $\text{II}$ is not correct explanation for statement $\text{I}$
• C. Statement $\text{I}$ is true but statement $\text{II}$ is false.
• D. Statement $\text{I}$ is false but statement $\text{II}$ is true.

Answer 1

The correct option is B Statement $\text{I}$ is true, statement $\text{II}$ is true but statement $\text{II}$ is not correct explanation for statement $\text{I}$

In Statement - $\text{I}$, $\overrightarrow{L}=I\overrightarrow{\omega }$ is the definition of the angular momentum for any rigid body.
In Statement - $\text{II}$, $\overrightarrow{\tau }=\frac{d\overrightarrow{L}}{dt}$ is also definition for torque but not the reason for the first statement, because it is not relating $\overrightarrow{L}$ to $\overrightarrow{\omega }$ and moment of inertia $I$ of rigid body.
$\therefore$ Option $\left(b\right)$ is correct.