Question

The mass of a rectangular plate of uniform thickness is $M$ and its length and breadth are $L$ and $\frac{L}{2}$ respectively. The expression for moment of inertia of same plate about an axis perpendicular to plane of plate and passing through one of four corners is:

• A. $\frac{M{L}^2}{12}$
• B. $\frac{M{L}^2}{3}$
• C. $\frac{5M{L}^2}{3}$
• D. $\frac{5M{L}^2}{12}$

Answer 1

The correct option is D $\frac{5M{L}^2}{12}$

Moment of inertia of rectangle $I=\frac{M(L^2+B^2)}{12}$ , now B=L/2

So we get $I_{cm}=\frac{5M{L}^2}{48}$

Now distance of center from the corner is $d=\sqrt{(L/2{)}^2+(L/4{)}^2}=\frac{\sqrt{5}L}{4}$,

So using parallel axis theorem $I=I_{cm}+M{d}^2=\frac{5M{L}^2}{48}+\frac{M\left(5L\right)}{16}$

$I=\frac{5M{L}^2}{12}$