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)`

A cube of coefficient of linear expansion `alpah` is floating in a bat

1.	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» 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`

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