1548067539635..jpg A solid cube is first floating in a liquid. The coefficient of linear expansion of cube is alpha and the coefficient of volume expansion of liquid is gamma. On increasing the temperature of (liquid + cube) system, the cube will sink if

Answers (1)
A Avinash Dongre


In the question as the cube is initially just floating the density of the cube=density of water

Afterwards when the temperature is increased ;

The increase in volume of water is proportional to \gamma

The increase in volume of cube is proportional to the volume expansion coefficient of cube I.e 3\alpha

So for water Vfinal =Vinitial .(1+\gamma)

For cube Vfinal =Vinitial.(1+3\alpha)

(V is volume)

So as the mass is constant

For water Dfinal of water=Dinitial/(1+\gamma)

For cube Dfinal of cube=Dinitial/(1+3\alpha)

Cube will sink if Dfinal of cube>Dinitial of water

I.e Dinitial /(1+3\alpha)>Dinitial/(1+\gamma)

As Dinitial is same for both

  \frac{1}{3\alpha }> \frac{1}{\gamma }\Rightarrow \gamma > 3\alpha