# 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

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

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

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