Question

Two masses each of mass $M$ are attached to the end of a rigid massless rod of length $L$. The moment of inertia of the system about an axis passing through centre of mass and perpendicular to its length is

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

Answer 1

Answer: (B)

The moment of inertia of the system about the given axis is

$I=M(\frac{L}{M}{)}^2+M(\frac{L}{2}{)}^2$
$=\frac{M{L}^2}{4}+\frac{M{L}^2}{4}=\frac{M{L}^2}{2}$