Question

A hollow cylinder has mass m outside radius r2 and inside radius r1 the moment of inertia about an axis parallel to its symmetrical axis and tangential to the outer surface

Answer 1

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Answer 2

Mass of the cylinder =  m

Outside radius = r₂

Inside radius = r₁

So the axis parallel to its symmetrical axis ( through its centre) and tangential to the outer surface means an axis on the outer surface through the length of the cylinder.

Moment of inertia on the symmetrical axis I₁ = (m/2) (r₁² + r₂²)

Following the parallel axis theorem, moment of inertia on the mentioned axis, I₂ = I₁ + mr₂² [ mass x distance from symmetrical axis ]

that is, I₂ = (m/2) (r₁² + r₂²) + mr₂²

or, I₂ = m [ (r₁²/2) + {(r₂²/2) + r₂²}

or I₂ = (m/2) [ r₁² + 3r₂² ]

So the answer is (m/2) (r₁² + r₂²)