Question

A square plate of uniform thickness has moment of inertia I about an axis passing through its center mass and perpendicular to its plane. Now it is cut in to four identical square plates. The moment of inertia of each of the smaller plates, about an axis passing through its center of mass and perpendicular to its plane is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

A square plate of side length 'a' and of mass M has the moment of inertia, $I=\frac{M{a}^2}{2}$

After cutting into four identical parts, each part will have the mass $\frac{M}{4}$ and it is of side length $\frac{a^2}{2}$

$\therefore$ It's moment of inertia $=I^1=\frac{\left(\frac{M}{4}\right)(\frac{a}{2}{)}^2}{6}$

$\Rightarrow I^1=\frac{1}{16}\frac{M{a}^2}{6}$

$\Rightarrow I^1=\frac{I}{16}$