# Volume expansion of the strange liquid

**Question:**

At ship floats with !!40%!! submerged when at !!100K!! and !!80%!! submerged when at !!150K!!. Coeff of volume expansion of liquid is?

- 0.02
- 0.005
- 0.0075

**Soltuion**

This is a simple question about the expansion of liquids, we know the two temperatures, so we know the initial volume and final volume of the liquid we will be able to solve the question.

Let the mass of the ship be !!M!!. Since the ship is floating the mass of liquid displaced is equal to the mass of the ship.

If !!V!! is the volume of ship, the volume of liquid displaced at !!100K!! and !!150K!! is !!0.4V!! and !!0.8V!!.

So !!0.4V!! is expanding into !!0.8V!!.

Hence we get !!0.8V=0.4V(1+DeltaT alpha)!!

!!=>2=1+(150-100)alpha!!

!!=> alpha=1/50=0.02!!