Question

(c) A solid weights 64N in air and 48N when totally immersed in a liquid 0.8g/cm3.

Answer 1

(a) When immersed in the liquid, the solid displaces an amount of liquid weighing 64 N - 48 N = 16 N, and this is the same as the magnitude of the buoyant force/upthrust.

(b) Archimedes' principle says the solid has a volume equal to that of the displaced liquid. At a density of 0.8 g/cm³ = 0.0008 kg/cm³, a 16-N amount of this liquid has a volume of

(16 N) / g × (1/0.0008 cm³/kg) = 2040.82 cm³

(c) Density is mass per unit volume, so you get the solid's density by dividing its mass (weight/g) by the volume in (b):

((64 N) / g) / (2040.82 cm³) ≈ 0.0032 kg/cm³ ≈ 3.2 g/cm³