A cube of coefficient of liear expansion `alpha_(s)` is floating in a bath containing a liquid of coefficient 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 the relation between `alpha_(s)` and `gamma_(L)` showing all the steps.

Explanation

When the temperature is increased, volume of the cube will increase while density of liquid will decrease. The depth upto which the cube is submerged in the liquid remains the same, hence the upthrust will not change. F = F.
`thereforeV_(1)rho_(L)g=V_(1).rho_(L).g" "(V_(1)="volume immersed")`
`therefore(Ah_(1))(rho_(L))(g)=A(1+2alpha_(s)DeltaT)(h_(1))xx(rho_(L)/(1+gammaDeltaT))g`
Solving this equation, we get `gamma_(1)=2alpha_(s)`