A metal solid sphere is rotating about an axis passing through its diameter, if its volume increased by 6% suddenly then its change in angular speed will be………

Options

A. decreased by 2%
B. increased by 2%
C. decreased by 4%
D. increased by 4%

Answer

C

Explanation

Volume `V=(4)/(3)piR^(3)`
`therefore (Deltav)/(v)=(3DeltaR)/(R)`
`therefore (DeltaR)/(R)=(1)/(3)((DeltaV)/(V))=(6)/(3)%=` increased by 2%
Moment of inertia `I=(2)/(5)MR^(2)`
`therefore IpropR^(2)`
`therefore (DeltaI)/(I)=(2DeltaR)/(R)` = increased by 4%
According to law of conservation of momentum
`Iomega` = constant
`therefore Iprop(1)/(omega)`
`therefore 4%` decreased in `omega`