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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 $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
A
$I_0 + ML^2$
B
$I_0 + \frac{ML^2}{2}$
C
$I_0 + \frac{ML^2}{4}$
D
$I_0 + 2ML^2$
Detailed Solution
The axis through the midpoint passes through the centre of mass, so $I_{CM} = I_0$.
The axis through one end is parallel to this axis and at a distance $h = \frac{L}{2}$ from it.
By the parallel axis theorem, $I = I_{CM} + Mh^2$
$I = I_0 + M\left(\frac{L}{2}\right)^2$
$I = I_0 + \frac{ML^2}{4}$
The axis through one end is parallel to this axis and at a distance $h = \frac{L}{2}$ from it.
By the parallel axis theorem, $I = I_{CM} + Mh^2$
$I = I_0 + M\left(\frac{L}{2}\right)^2$
$I = I_0 + \frac{ML^2}{4}$