Question

A cube of coefficient of linear expansion `alpah` is floating in a bath containing a liquid of coefficeient of volume expansion `gamma_(l)`. When the temperature is raised by `DeltaT`, the depth upto which the cube is submerged in the liquid remains the same. Find relation between `alpha` and `gamma_(l)`

Answer 1

Befor heating
`Mg = F_(b), Mg = V_(1)rho_(1)g = Axrho_(1)g` ……..(1)
After heating `Mg = F_(b)^(1), Mg = V^(1)rho_(1)^(1)g` ……(2)
Equating `(1)` & `(2) Axrho_(1)^(1)g`
`Arho_(1)g = A(l + betaDelta t)(rho_(1))/(1 + gammaDetla t)g`
`1 + gammaDelta t = 1 + betaDeltat, gamma = beta :. gamma = 2alpha`