Moment of inertia of a solid sphere about its diameter is I . If that sphere is recast into 8 identical small spheres, then moment of inertia of such small sphere about its diameter is

Options

A. `I//8`
B. `I//16`
C. `I//24`
D. `I//32`

Answer

D

Explanation

`"M = 8 m " therefore m=(M)/(8)`
Volume of big sphere = Volume of 8 spheres
`(4pi)/(3)R^(3)=8xx(4pi)/(3)r^(3)`
`R = 2 r`
`therefore " " r = (R )/(2)`
`I_(1)=(2)/(5)mr^(2)`
`= (2)/(5)mr^(2)`
`= (2)/(5)xx(M)/(8)xx((R )/(2))^(2)`
`= (2)/(5)MR^(2)xx(1)/(8)xx(1)/(4)`
`I_(1)=I xx(1)/(32)`.