An object floats in water with half of its volume immersed in water. What will be its relative density?
When a body floats in water, the upthrust it experiences is equal to the weight of the body.
Hence, upthrust (U) = Weight of the body
U=mg
(Where,m= mass of the body andg= acceleration due to gravity)
Mass (m) = Density (d) × Volume (V)
Therefore,
U=d×V×g...(1)
Upthrust is also equal to the weight of water displaced.
Volume of water displaced is
,Vbeing the volume of the object.
Therefore,
U= Mass of water displaced ×g
(whered w= density of water) ...(2)
Since the weight of the object is equal to the weight of the displaced water,
Therefore, the relative density of the object is
.
How do the densities of solid, liquid and gas vary with temperature?
Solids:All forms of matter expand on heating; but in solids, heating has very little effect on the volume of the solid. As a result, the density of a solid does not change much with variation of temperature.
Liquids and Gases:When liquids and gases are heated, their volume increases. As volume is inversely proportional to density, an increase in volume, results in a decrease in density. Hence, with the increase in temperature, densities of liquids and gases decrease and vice versa.
For object floats:
Archemedes' Principle. The upthrust on the body is equal to the weight of the water displaced.
Half of the body is immersed, it means it displaces a volume of water equal to half of it's own volume.
So, weight of water of half the volume of object would be equal to the weight of the object as it is floating.
Now go through the equations. This has been solved to get the answer.
For 8th
Density = Mass/Volume
What happens if you keep the mass same and increase the value of volume? The density would decrease, right? Yes.
The rest has been explained in the question.