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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

A

`x=sqrt(2/15) R`

B

`x = sqrt(2)/15` R

C

`x = 2/15 R`

D

`x=2/sqrt(15)` R

Text Solution

Verified by Experts

The correct Answer is:
D
`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`
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