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A spherical shell of mass M and radius R...

A spherical shell of mass `M` and radius `R` filed completely with a liquid of same mass and set to rotate about a vertical axis through its centre has a moment of inertia `I_(1)` about the axis. The bottom. If moment of inertia of the system is `I_(2)` when the shell is half filled and `I_(3)` is the moment of inertia when entire water drained off then :

A

`(I_(1))/(I_(2)) ~~ 1.5`

B

`(I_(1))/(I_(2)) ~~0.67`

C

`(I_(1))/(I_(3)) ~~ 1.6`

D

`(I_(2))/(I_(3)) ~~ 1.4`

Text Solution

Verified by Experts

The correct Answer is:
C
A spherical shell ………….
`(C ) I_(1) = (2)/(3)MR^(2)+(2)/(5)MR^(2)= (16)/(15)MR^(2)`
`I_(2) = (2)/(3) MR^(2)+(2)/(5)(M)/(2)R^(2)=(13)/(15)MR^(2)`
`I_(3)=(2)/(3)MR^(2)` , `(I_(1))/(I_(3)) = 1.6`
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