Question

Moment of inertia of a rod of mass $ M $ and length $ L $ about an axis passing through a point midway between centre and end is

• A. $ \frac{ML^2}{6} $
• B. $ \frac{ML^2}{12} $
• C. $ \frac{7ML^2}{24} $
• D. $ \frac{7ML^2}{48} $

Answer 1

Answer: (D)

$I=I_{C M}+M x^{2}$

$=\frac{M L^{2}}{12}+M\left[\frac{L}{4}\right]^{2}$
$=\frac{M L^{2}}{12}+\frac{M L^{2}}{16}$
$=\frac{7 M L^{2}}{48}$