Find the moment of inertia of a uniform rign of mass M and radius R about a diameter.

Options

A. `(MR^(2))/(4)`
B. `(MR^(2))/(2)`
C. `2MR^(2)`
D. `4MR^(2)`

Answer

B

Explanation

Let X and Y-axis be along two perpendicular diameter of the ring. By symmetry

`I_(X)=I_(Y) and I_(Z)=I_(X)+I_(Y)`
But we know that, `I_(Z)=MR^(2),MR^(2)=I_(X)+I_(Y)`
`MR^(2)=2I_(X), I_(X)=I_(Y)=(MR^(2))/(2)`