Question

Th moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through on edge of perpendicular to its length will be :-

• A. $\frac{M{L}^2}{12}$
• B. $\frac{M{L}^2}{6}$
• C. $\frac{M{L}^2}{3}$
• D. $M{L}^2$

Answer 1

The correct option is C $\frac{M{L}^2}{3}$

Given,

Mass of rod $=M$

Length of Rod $=L$

Distance of rods edge from center $=\frac{L}{2}$

Moment of inertia of rod at center $I_c=\frac{1}{12}M{L}^2$

For moment of inertia at edge apply parallel axis theorem. $I_e=I_c+M{\left(\frac{L}{2}\right)}^2$

$I=\frac{1}{12}M{L}^2+M{\left(\frac{L}{2}\right)}^2=\frac{1}{3}M{L}^2$

moment of inertia at edge is $\frac{1}{3}M{L}^2$