A body has masses of 0.013kg and 0.012 kg in oil and water respectively. If the relative density of oil is 0.875 calculate the mass of the body.

Let me work this out carefully, because the numbers need checking against the options.

Analyze the question The "masses" in oil and water are apparent masses (the mass reading when the body is submerged). The question asks for the actual mass of the body in air.

Concept By Archimedes' principle, loss in apparent mass = mass of liquid displaced.

Let m = true mass and V = volume of the body.

• In water: m − 0.012 = V × ρw
• In oil: m − 0.013 = V × ρo = V × 0.875 ρw

Solution Working in units where ρw = 1 (relative density), the loss in water is V and the loss in oil is 0.875V.

• m − 0.012 = V
• m − 0.013 = 0.875V

Subtract the second equation from the first:

0.001 = 0.125V, so V = 0.008 (in kg of water, i.e. 8 cm³)

Then m = 0.012 + 0.008 = 0.020 kg

Check: In oil: 0.020 − 0.875(0.008) = 0.020 − 0.007 = 0.013 kg ✓

Answer: The mass of the body is 0.02 kg, which is option A.

Tip: For these problems, always write "loss in weight = weight of fluid displaced" for each liquid, then use the two equations to eliminate the volume. Subtracting the equations is the quickest route. Also check your answer by substituting back into the second liquid.