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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

`r=(sqrt2)/(15)R`

B

`r=(2)/(sqrt(15))=R`

C

`r=sqrt((2)/(15))R`

D

`r=(2)/(15)R`

Text Solution

Verified by Experts

The correct Answer is:
B
The M.I. of a solid sphere about its any diameter is
`I=(2)/(5)MR^(2)" …(1)"`
When it is recasted into a disc of radisu r, its mass remains constant and M.I. about an axis through its edge and perpendicular to its plane is
`I=Mr^(2)+(Mr^(2))/(2)=(3)/(2)Mr^(2)" ...(2)"`
`therefore" From (1) and (2), "(2)/(5)MR^(2)=(3)/(2)Mr^(2)`
`r^(2)=(4)/(15)R^(2)" "therefore r=(2P)/(sqrt(15))`
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