Q156 / 180 · COMEDK 2024 (Memory Based) · Physics
Let $I_A$ and $I_B$ be moments of inertia of a body about two axes $A$ and $B$, respectively. The axis $A$ passes through the centre of mass of the body but $B$ does not, then .
- A$I_A \lt I_B$
- B$I_A \lt I_B$, whether the axes are parallel or not parallel
- Correct answerCif the axes are parallel $I_A \lt I_B$
- Dif the axes are not parallel $I_A \geq I_B$
Solution
$I_{\mathrm{CM}}$ is less than $I$ about any other axis not passing through centre of mass but only when two axes are parallel.
$\Rightarrow \quad I_B=I_A+I_A r^2$
where, $r$ is the distance between parallel axes.
$\therefore \quad I_A \lt I_B$
$\Rightarrow \quad I_B=I_A+I_A r^2$
where, $r$ is the distance between parallel axes.
$\therefore \quad I_A \lt I_B$
Hence, the correct answer is option: 'C'.