A solid weight 45N and 15N respectively in air and water. Determine the relative density of the solid
Answer Details
The relative density of a substance is defined as the ratio of its density to the density of a reference substance. In this case, the reference substance is water.
When the solid is in air, it experiences a weight of 45N. This means that the weight of the displaced air is also 45N. Therefore, the density of the solid is:
density of solid = weight of solid / volume of solid
Since the volume of the solid is the same in air and in water, we can write:
density of solid in air = weight of solid / volume of solid = weight of displaced air / volume of solid
When the solid is in water, it experiences a weight of 15N. This means that the weight of the displaced water is 45N - 15N = 30N. Therefore, the density of the solid is:
density of solid in water = weight of solid / volume of solid = weight of displaced water / volume of solid
Now, the relative density of the solid is defined as the ratio of the density of the solid to the density of water:
relative density of solid = density of solid / density of water
We can substitute the expressions we obtained for the densities of the solid in air and in water:
relative density of solid = (weight of displaced air / volume of solid) / (weight of displaced water / volume of solid)
Simplifying this expression, we get:
relative density of solid = weight of displaced air / weight of displaced water
Substituting the values we obtained for the weights of displaced air and water, we get:
relative density of solid = 45N / 30N = 1.5
Therefore, the relative density of the solid is 1.5.
Answer: 1.50