When the temperature of a body increases from t to `t+Deltat`, the moment of inertia of it increases from I to `I+DeltaI`. If the coefficient of linear expansion of the body is `alpha,` then show that `(DeltaI)/I=2alphaDeltat`.

Explanation

We know, moment of inertia `I=mk^(2)`
`therefore " "DeltaI=2mkDeltak`
`therefore " "(DeltaI)/I=(2mkDeltak)/(mk^(2))=(2Deltak)/k=(2alphakDeltat)/k " "[Deltak=alphakDeltat]`
`" "=2alphaDeltat`