(A) Let IAB be the M.I. of the given sphere about the diameter AB of radius R and mass m.
∴ IAB = 2/5 MR2 ....(i)
It means the sphere is solid
Let CD be a tangent of the sphere parallel to the diameter AB of the sphere.
∴ Distance between the two parallel axes is R. If ICD be is MI about CD axis, then according to the theorem of parallel axes,
ICD = IAB + MR2 = 2/5 MR2 + MR2 = 7/5 MR2
(b) Here AB and CD are the diameter sof the disc of radius R and mass M. Let EF be an axis ⊥ ar to the plane of disc and passing through a point D on its edge.
Clearly the axis DG is parallel to the axis EF
∴ If IEF be the M.I. of the disc about EF axis,
Then according to theorem of ⊥ ar axes.
IEF = IAB + ICD = {MR2}/{4} + {MR2}/{4} = 1/2 MR2
Here ⊥ ar distance between EF and DG axes = R
∴ If IDG be the M.I. of the disc about the required axes, then according to theorem of parallel axes.
IDG = IEF + MR2 = 1/2 MR2 + MR2 = 3/2 MR2