Question

The moment of inertia of a thin uniform rod of length $ L $ and mass $ M $ about an axis passing through a point at a distance of $ 1/3 $ from one of its ends and perpendicular to the rod is

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

Answer 1

Answer: (B)

$I_{ CM }=\frac{M L^{2}}{12} \,\,\,\,$ (about middle point)

$ \therefore \,\,\,I =I_{ CM }+M x^{2} $
$=\frac{M L^{2}}{12}+M\left(\frac{L}{6}\right)^{2} $
$I =\frac{M L^{2}}{9} $