Question

The radius of gyration of rod of length $L$ and mass $M$ about an axis perpendicular to its length and passing through a point at a distance $\frac{L}{3}$ from one of its ends is:

• A. $\frac{\sqrt{7}}{6}L$
• B. $\frac{L}{9}$
• C. $\frac{L}{3}$
• D. $\frac{\sqrt{5}}{2}L$

Answer 1

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

Moment of inertia of rod about cm ,$Icm=\frac{M{L}^2}{12}$

Distance of point from cm d=$l/2-l/3=l/6$,

So, Moment of inertia at that point $I=Icm+M{d}^2=\frac{M{L}^2}{12}+\frac{M{L}^2}{36}=\frac{M{L}^2}{9}$

So $M{L}^2/9=M{K}^2\Rightarrow K=L/3$