A uniform solid brass cylinder of mass `M = 0.5 Kg` and radius `R = 0.03 m` is placed in frictionless bearings and set to rotate about its geometrical axis with an angular velocity of `60 rad/s.` After the cylinder has reached the specified state of rotation, it is heated (without any mechanical contact) from room temperature `20^(0)C` to `100^(0)C`. The fractional change in angular velocity of the cylinder is `(alpha = 2 xx 10^(-5//0)C)`sss

Options

A. `-3.2 xx 10^(-3)`
B. `3.2 xx 10^(-3)`
C. `2.3 xx 10^(-3)`
D. `-2.3 xx 10^(-3)`

Answer

A

Explanation

`I_(1)omega_(1)=I_(2)omega_(2),(Deltaomega)/(omega)=(-DeltaI)/(I)=(-2Delta)/(R)-2alphaDeltat`
`[I prop R^(2), (DeltaI)/(I) = (2DeltaR)/(R)]`