Question

Four spheres each of mass M and diameter 2r, are placed with their centers on the four corners of a square of side a( gt 2r). The moment of inertia of the system about one side of the square is

Answer 1

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One of the sphere rotate about its own axis, thus its moment of inertia is given as 52ma2 and the moment of inertia of other three are found out using parallel axis theorem. Two of them are at a distance of b from the rotational axis the sum of their moment of inertia is 2×(52ma2+mb2) and the third one is at a diagonal distance of 2b, thus its moment of inertia is 52ma2+2mb2

Thus we get total moment of inertia as 54m[2a2+5b2]