Question

One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. it is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is

A. `(1)/(2)MR^(2)`
B. `(1)/(4)MR^(2)`
C. `(1)/(8)MR^(2)`
D. `sqrt2MR^(2)`

Answer 1

For the complete disc, `M.I.` about the axis `=(1)/(2)(4M)R^(2)`
For the quarter disc,
`M.I.=(1)/(4)[(1)/(2)(4M)R^(2)]`
`=(1)/(2)MR^(2)`