Moment of inertia of a circular wire of mass M and radius R about its diameter is

Options

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

Answer

A

Explanation

(a) M.I of a circular wire about an axis nn' passing throgh
the centre of the circule and perpendicular to the plane
of the circle = MR^2


As shown in the figure X-axis and Y -axis lie in the
plane fo the ring. Then by perpendicular axis theorem
`I_X + I_Y = I_Z`
`rArr 2I_X = MR^2 [:. I_X = I_Y (by symmetry) and I_Z = MR^2]`
`:. I_X = (1)/(2)MR^2`