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

Options

A. I
B. `(2I)/(3)`
C. `(I)/(5)`
D. `(I)/(10)`

Answer

(c)

Explanation

Moment of inertia of a disc, `I-(1)/(2) MR^(2)`
Volume of disc =Volume of sphere
`piR^(2)xx(R)/(6)=(4)/(3)xxpixxR_(1)^(3)`
Rightarrow`R_(1)^(3)=(R^(3))/(8)`
`R_(1)=(R)/(2)`
Moment of inertia of sphere,
`I=(2)/(5)MR_(1)^(2)=(2)/(5)M((R)/(2))^(2)=(2)/(5)(MR^(2))/(4)=(I)/(5)`