A disc of radius R and thickness has moment of inertia / about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is

Options

A. `l/5`
B. `l/6`
C. `l/32`
D. `l/64`

Answer

A

Explanation

According to question, Moment of inertia of disc is given by `l=(MR^2)/2`
[Symbals have their usual meanings.]
When the disc is remoulded into solid sphere, then volume remains same. i.e,Volume of disc =Valume of solid sphere
i.e `piR^2xxR/6=4/3pir^3`
`Rightarrow r^3=R^3/8 Rightarrow r=R/2`
Now, moment of inertia of solid sphere is given by `2/5mr^2`
`=2/5xxmxxR^2/4=(mR^2)/10`
`l/5` [l = moment of inertia of disc]