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, `(piR^(2))xx(R)/(6)=(4)/(3)pir^(3)`
`implies(R^(3))/(8)=r^(3)impliesr=(R)/(2)`
MOI of sphere, `I.=(2)/(5)Mr^(2)`
`I.=(2)/(5)M((R)/(2))^(2)=(1)/(5)(MR^(2))/(2)=(I)/(5)`