Question

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $0_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is :

• A. $0_0+\frac{M{L}^2}{2}$
• B. $0_0+\frac{M{L}^2}{4}$
• C. $0_0+2M{L}^2$
• D. $0_0+M{L}^2$

Answer 1

The correct option is B $0_0+\frac{M{L}^2}{4}$

Using Parallel Axis Theorem,
Moment of inertia about an axis passing through one of the rod ends(E) and perpendicular to its length $=$[ moment of inertia of a about an axis passing through its midpoint (o) and perpendicular to its length $+$ (total mass of the rod $\times$ square of distance between points o and E.)]
$\therefore I_E=I_o+M(\frac{L}{2}{)}^2=0_0+\frac{M{L}^2}{4}$