To measure the relative density of a solid by using Archimedes’ principle
On page 101 we explained the meaning of the term relative density, and its importance in the accurate measurement of density.
By definition, mass of any volume of the substance relative density of a substance = mass f I I f 0 an equa volume 0 water or since, at any particular place, the mass of anything is proportional to its weight, weight of any volume of the substance relative density of a substance. weig t 0 an equa volume 0 water The weighings required on the right hand side of this equation are best obtained by an experiment using Archimedes’ principle. We weigh a sample of the solid, first in air, and then in water. The apparent loss in weight, obtained by subtraction, is equal to the weight of a volume of water equal to that of the sample.
If weight of a sample of the substance re anve density 0 a substance = the apparent loss III weight of the sample III water Weighing may be carried out using a spring balance calibrated in newtons. More accurately, a beam or lever balance may be used. However, these measure mass, not weight, so the mass readings must be multiplied by g, the acceleration due to gravity, at the place of the experiment (see page 68). This creates no problem since as we shall see, the value of g disappears from the final calculation, so we do not have to know its value. Methods of weighing a body in water are shown in Fig. 12.3 or 12.4. A wooden or aluminium bridge is placed over the left-hand pan of the balance, care being taken to see that the pan does not touch it as it swings. The sample, e.g., a piece of brass, is then tied by thin-thread to the lower hook of the balance stirrup so that it hangs just clear of the top of the bridge. The brass is then weighed. A beaker containing water is then placed on the bridge so that the brass is completely immersed and does not touch the side of the beaker. Having made certain that there are no air bubbles clinging to the brass, it is weighed in water. If rn I and rn 2 are the mass readings obtained in these two weighings, then