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 vertex is _____ kgm².

Solution

Physics sir · 2 steps

The axis sits on one corner, so measure each particle's distance from that corner, not from the centre.

1. Point masses. For point masses, I = Σ m r², where r is each particle's perpendicular distance from the axis. Here the axis passes through one corner, perpendicular to the square.

   Particle	Distance from axis	m r²
   On the axis corner	0	0
   Adjacent corner	2 m	1 × 2² = 4 kg m²
   Other adjacent corner	2 m	1 × 2² = 4 kg m²
   Opposite corner	diagonal, 2√2 m	1 × (2√2)² = 8 kg m²

   I = 0 + 4 + 4 + 8 = 16 kg m²

2. So. The moment of inertia about the corner axis is 16 kg m².

The common slip: 8. Using the distance from the centre of the square, √2 m, for every particle gives 8, which is the moment of inertia about the centre, not about a corner.

The idea to keep. For particles, I is just Σ m r². Always measure r from the given axis, and remember the particle on the axis contributes nothing.

Answer from the NTA final answer key. Solution by PrepWiser.