A cube of coefficient of linear expansion alpha_(s) is floating in a bath containing a liquid of coefficient of volume expansion gamma_(1). 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)andgamma_(1) showing all the steps. 1) gamma=alpha_(s) 2) gamma=3alpha_(s) 3) 2gamma=alpha_(s) 4) gamma=2alpha_(s)

A cube of coefficient of linear expansion alpha_(s) is floating in a b

1.	A cube of coefficient of linear expansion alpha_(s) is floating in a bath containing a liquid of coefficient of volume expansion gamma_(1). 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)andgamma_(1) showing all the steps. 1) gamma=alpha_(s) 2) gamma=3alpha_(s) 3) 2gamma=alpha_(s) 4) gamma=2alpha_(s)
Answer» Solution :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)`