Question:
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
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Two spheres have their centres on the axis; the other two are at distance \(b\). Use \(I=\frac25ma^2\) and the parallel axis theorem.
Updated On: Nov 4, 2026
- \(\frac{4}{5}ma^2\)
- \(\frac{8}{5}ma^2+mb^2\)
- \(\frac{4}{5}ma^2+2mb^2\)
- \(\frac{8}{5}ma^2+2mb^2\)
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The Correct Option is D
Solution and Explanation
Axis along one side of the square: two sphere centres lie on the axis, two are at perpendicular distance \(b\).
Each sphere about its diameter: \(\frac25ma^2\).
Two on the axis: \(2\times\frac25ma^2=\frac45ma^2\).
Two at distance \(b\) (parallel axis theorem): \(2\left(\frac25ma^2+mb^2\right)=\frac45ma^2+2mb^2\).
Total \(I=\frac85ma^2+2mb^2\).
Answer: (4) \(\frac{8}{5}ma^2+2mb^2\)
Each sphere about its diameter: \(\frac25ma^2\).
Two on the axis: \(2\times\frac25ma^2=\frac45ma^2\).
Two at distance \(b\) (parallel axis theorem): \(2\left(\frac25ma^2+mb^2\right)=\frac45ma^2+2mb^2\).
Total \(I=\frac85ma^2+2mb^2\).
Answer: (4) \(\frac{8}{5}ma^2+2mb^2\)
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