A solid sphere of mass M and radius R having tmoment of inertia I about its diameter is recast into a solid dise of radius r and thickness t. The moment of inertia of the disc about an axis passing the edge and perpendicular to the plane remains I. Then R and r are related as

Options

A. `r= sqrt((2)/(15))R`
B. `r=(2)/(sqrt(15))R`
C. `r=(2)/(15)R`
D. `r=(sqrt(2))/(15)R`.

Answer

B

Explanation

Given moment of inertia of sphere can be written as follows:
`I=(2)/(5)mR^(2)" "......(i)`
Mass of the disc is also m and moment of inertia about the described axis can be written using parallel axis theorem.
`I=(1)/(2)mr^(2)+mr^(2)=(3)/(2)mr^(2)" ".....(ii)`
Moments of inertia given by equations (i) and (ii) are equal.
`(2)/(5)mR^(2)=(3)/(2)mr^(2)`
`r=(2)/(sqrt15)R`
Option (6) is correct.