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What is the moment of inertia of a solid...

What is the moment of inertia of a solid sphere of density `rho` and radius R about its diameter ?

A

`(105)/(176)R^(5)rho`

B

`(105)/(176)R^(2)rho`

C

`(176)/(105)R^(5)rho`

D

`(176)/(105)R^(2)rho`

Text Solution

Verified by Experts

The correct Answer is:
C
Moment of inertia of sphere about it diameter `I=(2)/(5)MR^(2)=(2)/(5)((4)/(3)piR^(3)rho)R^(2)["As "M=Vrho=(4)/(3)piR^(3)rho]`
`l=(8pi)/(15)R^(5)rho=(8xx22)/(15xx7)R^(5)rho=(176)/(105)R^(5)rho`
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