Ring of non-uniform density

Classical Mechanics Level 5

A rod of length 2πR has non uniform density such that density at a point can found by multiplying a constant \(\delta\) to the distance of the point from the nearer end. This implies that density at end points is zero and is maximum at centerof rod.

Now this rod is bent to form a circular ring (max and zero density points are dimetrically opposite).

Find the moment of inertia of the ring about an axis passing through the point of zero density and perpendicular to plane of ring.

Details and Asumptions

\(\bullet\) \(\text{R=10, \delta = 5}\)

\(\bullet\) input first 6 digits of the answer

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