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. `(l)/(32)`
B. `(l)/(16)`
C. `(l)/(6)`
D. `(l)/(4)`

Answer

A

Explanation

Moment of inertia of big drop is `l=(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)`
`rArr" "n^(1//3)r=R" as "n=8 rArr =r=(R)/(2)`
Mass of each small droplet `=(M)/(8)`
`therefore` Moment of inertia ofo each small droplet
`=(2)/(5)[(M)/(8)][(R)/(2)]^(2)`
`=(1)/(32)[(2)/(5)MR^(2)]=(l)/(32)`