Question

An object has a mass in air of 0.0832 kg, apparent mass in water of 0.0673 kg, and apparent mass in another liquid of 0.0718 kg. What is the specific gravity of the other liquid?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of water = ₁ = 1000 kg/m³

Density of the other liquid = ₂

Mass of the object in air = m = 0.0832 kg

Volume of the object = V

Apparent mass of the object in water = m₁ = 0.0673 kg

Buoyancy force on the object in water = F_b1 = ₁Vg

mg = m₁g + F_b1

mg = m₁g + ₁Vg

m = m₁ + ₁V

0.0832 = 0.0673 + (1000)V

V = 1.59 x 10^-5 m³

Apparent mass of the object in the other liquid = m₂ = 0.0718 kg

Buoyancy force on the object in the other liquid = F_b2 = ₂Vg

mg = m₂g + F_b2

mg = m₂g + ₂Vg

m = m₂ + ₂V

0.0832 = 0.0718 + ₂(1.59x10^-5)

₂ = 717 kg/m³

Specific gravity of the other liquid = s

s = 0.717

Specific gravity of the other liquid = 0.717