The M.1. of a solid sphere about its diameter is I. It is then casted into 8 small identical spheres. What is the M.I. of each small sphere about its diameter?

Options

A. `(1)/(8)`
B. `(1)/(24)`
C. `(1)/(16)`
D. `(1)/(32)`

Answer

D

Explanation

`V=(4)/(3)piR^(3)=((4)/(3)pir^(3))xx8" "therefore" "r=(R)/(2)`
`I=(2)/(5)MR^(2)` for the original solid sphere
For the small sphere, `M'=(M)/(8) and r=(R)/(2)`
`therefore" "I'=(2)/(5)((M)/(8))((R)/(2))^(2)=(2)/(5)(MR^(2))/(32)=(1)/(32)`