Question

How can you determine the relative density of a substance using Archimedes principle
A. Relative density of a substance$ = $weight of sample of the substance/ apparent loss in weight of the sample in water.
B. Relative density of the substance$ = $ apparent loss in weight of the sample in water/ weight of sample of the substance.
C. Relative density of the substance$ = $ weight of sample of the substance/ weight of the sample in water.
D. Relative density of the substance$ = $ weight of the sample in water/ weight of sample of the substance.

Answer 1

HintUse the definition of relative density and Archimedes principle to deduce the expression. Balance the forces on the body which is immersed in water to find the buoyant force.

 Complete step-by-step solution
Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the centre of mass of the displaced fluid. Archimedes' principle is a law of physics fundamental to fluid mechanics.
We know that,
Relative density of a substance is equal to the ratio of density of the substance and the density of water at ${4^0}C$.
But,
From Archimedes principle
When an object is immersed in a liquid, the liquid exerts an upward force, which is known as the buoyant force, that is proportional to the weight of the displaced liquid. The sum force acting on the object, then, is equal to the difference between the weight of the object.
From here, we can conclude that,
Relative density of a substance$ = $weight of sample of the substance/ apparent loss in weight of the sample in water.

Additional information:
Difference between density and relative density.
Density is mass divided by volume. It is denoted by the Greek letter $\rho $.
Relative density is comparison of density of the substance with that of water. Relative density is a pure density with no unit because it is a ratio of densities of different substances. Density of water being one gm. per cc the numerical value of density and relative density is the same. The numerical value of relative density is the same in all systems.

Note:- The values of relative densities of different substances are only calculated with respect to the density of water at four degree Celsius only. This is because the density of water increases up to four degree Celsius and decreases above this temperature.