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A circular disc of radius R and thicknes...

A circular disc of radius `R` and thickness `R//6` has moment of inertia `I` about an axis passing through its centre and perpendicular to its plane. It is melted and recast into a solid sphere. The `M.I` of the sphere about its diameter as axis of rotation is

A

I

B

`(2I)/(8)`

C

`(I)/(5)`

D

`(I)/(10)`

Text Solution

Verified by Experts

The correct Answer is:
C
`I= (MR^(2))/(2)`
Now, `(pi R^(2)) xx (R)/(6) = (4)/(3) pi r^(3)`
`rArr (R^(3))/(8) = r^(3) rArr r= (R)/(2)`
MOI of sphere, `I.= (2)/(5) Mr^(2)`
`I. = (2)/(5) M ((R)/(2))^(2)= (1)/(5) (MR^(2))/(2)= (I)/(5)`
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