Question

The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of $x$ from it, is $I\left(x\right)$. which one of the graphs represents the variation of $I\left(x\right)$ with $x$ correctly?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

According to parallel axes theorem

$I\left(x\right)=I_{cm}+m{x}^2$

$\Rightarrow I\left(x\right)=\frac{2}{5}m{R}^2+m{x}^2$

$\text{As}I\left(x\right)\propto x^2$, the graph will be a parabola.

$\text{Here, at}x=0\to I\left(x\right)=\frac{2}{5}m{R}^2$

Hence, graph $\left(4\right)$ correctly depicts $I\left(x\right)$ vs $x$