Moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane is 'I'. The ratio of moment of inertia about a parallel axis tangential to its rim to passing through a point midway between the centre and the rim is

Step-by-step solution

I = MR ^2 2 M.I. of disc about an axis passing through centre of mass By parallel axis theorem, M.I for axis tangential to rim, I ₁= MR ^2 2 + MR ^2= 3 2 MR ^2 M.I for axis passing through a point midway between centre and rim (h=R / 2) , aligned & I ₂= MR ^2 2 + MR ^2 4 = 3 4 MR ^2 & I ₁ I ₂ = 3 2 MR ^2 3 4 MR ^2 = 2 1 2: 1 aligned