Question

33. Four particles, each of mass m, are arranged at
the corners of a massless square of side a. The
M.I. of system about an axis, which is
perpendicular to plane of square and passes
through one corner is
(1) ma^2
(2) 4ma^2
(3) ma²/4

(4) 2ma^2​

Answer 1

Answer:

2ma^2.

Explanation:

Since, we know that the length of the diagonals are a√2 and the half of the diagonals or the length from the center to any corner of the square will be a√2/2 which on solving we will get a/√2. Where a is the side length of the square which is given.

So, the moment of inertia will be when the 4 particles are present so the mass will be 4m. So, the moment of inertia will be 4mr^2 or 4md^2 which will be 4m[a/√2]^2 which on solving we will get 2ma^2.

Answer 2

Answer: 4ma^2

Explanation: