Question

$I$ is moment of inertia of a thin rod of mass $M$, length $L$ about an axis perpendicular to the length of rod and passing through its centre. The moment of inertia of a thin square plate of mass $4M$, side length $\frac{L}{2}$ about an axis passing through opposite corners of plate is:

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

Answer 1

The correct option is C $I$

For thin rod of mass $M$ and length $L$ :

Moment of inertia about axis perpendicular to the length of rod and passing through its centre is $I=M{L}^2/12$

For thin square plate of mass $M^{\prime }=4M$ and side length $L^{\prime }=L/2$:

Moment of Inertia about axis passing through opposite corners $I^{\prime }=\frac{M^{\prime }(L^{\prime }{)}^2}{12}$

$\therefore$ $I^{\prime }=\frac{\left(4M\right)(L/2{)}^2}{12}=M{L}^2/12=I$