The relative density of a liquid is the ratio of the

1. Analyze the question

The question asks for the definition of "relative density" (also known as specific gravity) in the context of a liquid. You need to identify which ratio correctly represents this physical property.

2. Explain the concept

Relative density is a dimensionless quantity that compares the density of a substance to the density of a reference substance (usually water for liquids and solids).

The formula is:

According to Archimedes' Principle, the upthrust (buoyant force) experienced by an object fully immersed in a fluid is equal to the weight of the fluid displaced.

• Upthrust in liquid ($U_L$) = $V \times \rho_L \times g$
• Upthrust in water ($U_W$) = $V \times \rho_W \times g$

If you take the ratio of the upthrust in the liquid to the upthrust in water:

This ratio is exactly the definition of relative density.

3. Show the solution

• Option A: This is the inverse of the density ratio.
• Option B: As shown in the derivation above, the ratio of the upthrust in the liquid to the upthrust in water is equal to the ratio of their densities, which is the definition of relative density.
• Option C: This is the inverse of the definition of relative density.
• Option D: This is the inverse of the ratio in Option B.

Comparing our derivation to the options, Option B is the correct physical representation.

4. Identify the answer

The correct option is B.

5. Tip

When dealing with "Relative Density" questions, always remember the "Reference" is the denominator. Since we are finding the relative density of a liquid, water is the reference, so water must be the denominator in the density ratio. Because upthrust is directly proportional to density, the ratio of upthrusts follows the same pattern as the ratio of densities.