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

Options

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

Answer

D

Explanation

`I_(AB) = 25 MR^(2) = I`(given)
`I_(A'B') = I_(YY') + Mr^(2) =1/2Mr^(2) +Mr^(2) =3/2 Mr^(2) = I`(given)
………….(iii)

From Eqs. (i) and (ii), `2/5 MR^(2) = 3/2 MR^(2) rArr r=2/sqrt(15)R`