Question

The moment of inertia of a semicircular ring of mass M and radius R about an axis which is passing through its centre and at an angle `theta` with the line joining its ends as shown in figure is

A. `(MR^(2))/(4) iftheta =0^(@)`
B. `(MR^(2))/(2) if theta =0^(@)`
C. `(MR^(2))/(2)if theta =` any angle
D. `(MR^(2))/(2) if theta=90^(@)`

Answer 1

Correct Answer - C
If we complete the ring, its mass become 2m
. `:. I_("whole ring")=(1)/(2)(2M)(R^(2))=MR^(2)`
`(I_("whole ring") = MI "about any diameter")`
`:. I_("Half ring")=(1)/(2)(MR^(2))`
This value is independent of angle `theta`.