(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be `2 MR^(2)//5, where M` is the mass of the sphere and `R` is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass `M` and radius `R` about any of its diameters to be `(1)/(4)MR^(2)`, find the moment of inertia about an axis normal to the disc passing through a point on its edge.

Options

A. `(8)/(5)MR^(2)`
B. `(7)/(5)MR^(2)`
C. `(5)/(2)MR^(2)`
D. `(8)/(2)MR^(2)`

Answer

B

Explanation

Given moment of inertia of sphere about an axis through its centre is `(2)/(5)MR^(2)`.

Distance between a tangent and centre axis is R.
Using theorem of parallel axes.
Moment of inertia about a tangent
= Moment of inertia about an axis through the centre of mass `+Mh^(2)` (where, h = distance between axes)
`=(2)/(5)MR^(2)+MR^(2)=(7)/(5)MR^(2)" [given, h = R]"`