A rod AB of length l is pivoted at an end A and freely rotated in a horizontal plane at an angular speed `omega` about a vertical axis passing through A. If coefficient of linear expansion of material of rod is `alpha`, find the percentage change in its angular velocity if temperature of system is incresed by `DeltaT`

Explanation

It temperature of surrounding increases by `DeltaT`, the new length of rod beocmes
`l'=l(1+alpha DeltaT)`
Due of change in length, moment of inertia of rod also changes and it is about and end A and is given as `I_(A)^(')=(Ml^(-2))/3`
As no external force or torque is acting on rod thus its angular momentum remains constant during heating thus we have
`I_(A)omega=I_(A)^(')omega'`
[If `omega'` is the final angualr velocity of rod after heating]
or `(Ml^(2))/3 omega=(Ml^(2)(1+alpha DeltaT)^(2))/3 omega'`
or `omega'=omega(1-2alphaDeltaT)`
[Using binomial expansion for small `alpha`]
Thus percentage change in angular velocity of rod due to heating can be given as
`Delta omega=(omega-omega')/(omega)xx100%`
`=2 alpha Delta Txx100%`