JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Rotational Mechanics

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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 ______

kgm^{2}

Answer: 16

Solution

Taking the axis through one vertex, perpendicular to the square's plane, the distances of the four

1

kg masses from that vertex are

0

a

a

, and

a 2

(with

a = 2

m):

I = 0 + m a^{2} + m a^{2} + m (2 a^{2}) = 4 m a^{2} = 4 \times 1 \times 4 = 16 kg m^{2}

JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Integer answer

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