Question

Four point size bodies each of mass $M$ are fixed at 4 corners of light square frame whose side length is $L$. The moment of inertia of 4 bodies about an axis perpendicular to plane of frame and passing through any corner of frame is:

• A. $2M{L}^2$
• B. $2\sqrt{2}M{L}^2$
• C. $3M{L}^2$
• D. $4M{L}^2$

Answer 1

Answer: (D)

$4M{L}^2$

Length of the diagonal of square is d=$L\sqrt{2}$

So two masses are at the distance of L and one is at D from axis of rotation.

$I=M{L}^2+M{L}^2+M{d}^2=4M{L}^2$