A circular disc of radius `R` and thickness `R//6` has moment of inertia `I` about an axis passing through its centre and perpendicular to its plane. It is melted and recast into a solid sphere. The `M.I` of the sphere about its diameter as axis of rotation is

Options

A. I
B. `(2I)/(8)`
C. `(I)/(5)`
D. `(I)/(10)`

Answer

C

Explanation

`I= (MR^(2))/(2)`
Now, `(pi R^(2)) xx (R)/(6) = (4)/(3) pi r^(3)`
`rArr (R^(3))/(8) = r^(3) rArr r= (R)/(2)`
MOI of sphere, `I.= (2)/(5) Mr^(2)`
`I. = (2)/(5) M ((R)/(2))^(2)= (1)/(5) (MR^(2))/(2)= (I)/(5)`