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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Physics (PH)
Four solid sphere A,B,C,D each of mass M and radius a are placed with their centre on the four corners of a squar of side b each.calcuate moment of inertia of
four solid sphere A,B,C,D each of mass M and radius a are placed with their centre on the four corners of a squar of side b each.calcuate moment of inertia of systems abput one side and about a diagonal
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Somnath
moment of inertia of a solid sphere about an axis passing through its centre is 2/5Ma^2.If you look at the sphere no 2 and 3 then their total moment of inertia about CD axis is 2×2/5Ma^2.But we have to find moment of inertia of this two sphere about AB axis.To find it you can use parallel axis theorem.Mb^2 term comes from here and 2Mb^2 is due to two sphere.For better understanding see the parallel axis theorem.Parallel Axis Theorem Parallel axis theorem is applicable to bodies of any shape. The theorem of parallel axis states that the moment of inertia of a body about an axis parallel to an axis passing through the centre of mass is equal to the sum of the moment of inertia of body about an axis passing through centre of mass and product of mass and square of the distance between the two axes. IZ’ = Iz + Mα² where, α is the distance between two axes.