Moment of inertia of big drop is l. If 8 droplets are formed from big drop, then moment of inertia of small droplet is

Options

A. `(I)/(32)`
B. `(I)/(16)`
C. `(I)/(8)`
D. `(I)/(4)`

Answer

A

Explanation

Moment of inertia of big drop is `I=(2)/(5) MR^(2)`
When small droplets are formed from big drop volume of liquid remain same
` n(4)/(3)pir^(3)=(4)/(3)piR^(3)`
`implies n^(1//3) r=lR" as " n=8 implies r=(R)/(2)`
Mass of each small droplet `=(M)/(8)`
`:.` Moment of inertia of each small droplet
`=(2)/(5)[(M)/(8)][(R)/(2)]^(2)`
`(1)/(2)[(2)/(5)MR^(2)]=(I)/(32)`