Question

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is ${90}^0$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is :

• A. $\frac{M{L}^2}{6}$
• B. $\frac{\sqrt{2}M{L}^2}{24}$
• C. $\frac{M{L}^2}{24}$
• D. $\frac{M{L}^2}{12}$

Answer 1

The correct option is A $\frac{M{L}^2}{6}$

Moment of inertia of the system
$I=\frac{M(L/2{)}^2}{3}+\frac{M(L/2{)}^2}{3}$

$=\frac{M{L}^2}{12}+\frac{M{L}^2}{12}=\frac{M{L}^2}{6}$