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 centre of the original disc. It 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. `sqrt(2) MR^(2)`
.A. `(1)/(2) MR^(2)`
B. `(1)/(4) MR^(2)`
C. `(1)/(8) MR^(2)`
D. `sqrt(2) MR^(2)`
.
Correct Answer – A
Mass of the whole disc `= 4 M`
Moment of inertia of the disc about the given axis.
`(1)/(2) (4M) R^(2) = 2MR^(2)`
:. Moment of inertia of quarter section of the disc.
=`(1)/(4) (2MR^(2)) = (1)/(2) MR^(2)`.