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Four spheres each having mass m and radius r are placed with their centres on the four corners of a square of side a. Then the moment of inertia of the system about an axis along one of the sides of the square is

a
85mr2
b
85mr2+ma2
c
85mr2+2ma2
d
45mr2+4ma2

detailed solution

Correct option is C

IAB = I1AB+I2AB+I3AB+I4AB       = 25mr2+25mr2(25mr2+ma2)+(25mr2+ma2)       = 85mr2+2ma2

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