Question

Moment of inertia $I$ of a solid sphere about an axis parallel to a diameter and at a distance $x$ from its centre of mass varies as

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Using parallel axis theorem,
$I$ about axis parallel through diameter and at distance $x$ from COM$=I_C+m{x}^2$
where $m=$ mass of sphere
$I_C=$Moment of inertia about diameter

$I=I_C$ at $x=0$
$I$ versus $x$ graph is a upward parabola with minimum value of $I=I_C$ at $x=0$. Therefore, the correct graph is (a).