Question

Four point masses m, 2m, 3m and 4m are kept at the corners A, B, C and D respectively of a square ABCD of side '\(b\)'. The moment of inertia of the system about an axis perpendicular to the plane of the square and passing through the point D is

• A. \(12 mb^2\)
• B. \(10 mb^2\)
• C. \(8 mb^2\)
• D. \(5 mb^2\)

Hint:

Add \(mr^2\) for each mass, with \(r\) measured from the axis through D.

Answer 1

The Correct Option is C

Step 1: Set up coordinates
Put D at the origin, A at $(0,b)$, C at $(b,0)$ and B at $(b,b)$.

Step 2: Sum $mr^2$
$m(b^2)+2m(2b^2)+3m(b^2)+4m(0)=8mb^2$, option (C).

Final Answer:
$I=8mb^2$, option (C). \[ \boxed{8mb^2} \]