The surface density (mass/area) of a circular disc of radius a depends on the distance from the centre as rho(r)=A+Br. Find its mment of inertia about the line perpendicular to the plane of the disc through its centre.
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Explanation:
For a small elemental ring of width dx
⇒dI=dMx2
=(A+Bx)2πxdxx2
=(2πAx3+2πBx4)dx
=[2πAx4+52πBx4]09
=2πAa4+52πBa5
Hence, solved.
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