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Question

# A system of solid discs, each of mass M and radius R is shown in figure. Find the MOI about an axis passing through point O and perpendicular to the plane.

A
9MR22
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B
9MR2
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C
18MR2
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D
27MR2
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Solution

## The correct option is D 27MR2This is a regular hexagon made by joining all the disc centers whose every edge is equal to 2R. The moment of inertia of solid disc about its center and perpendicular to its plane is I=MR22 Here, distance of each of the points from point O is 2R each. Hence MOI will be same for all the discs about point O. Therefore, I=I1+I2+I3+I4+I5+I6 I=6×I1 I=6×[MR22+M(2R)2] I=6×[9MR22] I=27MR2

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