Question

The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is

• A. $\frac{7\, M \,L^{2}}{48}$
• B. $\frac{M L^{2}}{9}$
• C. $\frac{ML^{2}}{12}$
• D. $\frac{M{L^{2}}}{3}$

Answer 1

Answer: (B)

$\frac{M L^{2}}{9}$

Answer 2

The moment of inertia about middle point

$I_{C M}=\frac{M L^{2}}{12}$
From theorem of parallel axis theorem
$\therefore I=I_{C M}+M x^{2}$
$=\frac{M L^{2}}{12}+M\left(\frac{L}{6}\right)^{2}$
$=\frac{M L^{2}}{9}$