Question

A thin rod has a length of $5\text{m}$. What is the ratio of the $\text{MI}$ of the rod about an axis perpendicular and passing through it's centre, to $\text{MI}$ of the rod about an axis perpendicular and passing through one of the edges of the rod?

• A. $\frac{1}{4}$
• B. $4$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{1}{4}$

Length of rod $L=5\text{m}$
$\Rightarrow$Moment of inertia of the rod about an axis passing through the centre of the rod & $\perp$ to it's plane:
$I_C=\frac{M{L}^2}{12}$
Moment of inertia about an axis passing through one of the edges of the rod:
$I_E=\frac{M{L}^2}{3}$

$\therefore \frac{I_C}{I_E}=\frac{\left(\frac{M{L}^2}{12}\right)}{\left(\frac{M{L}^2}{3}\right)}=\frac{3}{12}=\frac{1}{4}$