Question

Four particles each of mass 1 kg are placed at four corners of a square of side 2 m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertices is _____ kgm2.

Answer 1

Consider a square of side 2 m. For each mass located at distances:

$I = ma^2 + ma^2 + m(2a)^2 + m(2a)^2$

$= 1 \times 2^2 + 1 \times 2^2 + 1 \times 4 + 1 \times 4 = 4 + 4 + 4 + 4 + 8 = 16 \, \text{kg m}^2$