I cant figure out how to set this up?

Question

You are asked to ind the density of a liquid. you take an iron sphere of diameter 10cm (density of iron 7800kg/m^3). you measure the weight of the sphere using a spring balance. when the sphere is completely inside the liquid the spring balance reads 30N. Calculate the density of the liquid.

Will an aluminium block (density of aluminium 2700 kg/m^3) of mass 0.5kg sink or float in the liquid?

Answer 1

Favorite Answer

The radius of the iron sphere is 5 cm = 0.05 m. (Note that there is a required space between a coefficient and its unit: "10 cm", not "10cm".)

The volume of the sphere is then ⁴/₃πr³ = ⁴/₃π(0.05 m)³ = ⁴/₃π(1.25 × 10ˉ⁴ m³)

≈ 5.24 × 10ˉ⁴ m³. Its mass is then 4.08 kg, and in air it weighs 40 N.The volume of the sphere is the volume of the displaced liquid, whose buoyant force offsets (40 N - 30 N) = 10 N of the sphere's weight.Therefore the weight of the displaced liquid is 10 N, and its mass is 1.02 kg -- which means that its density is (1.02 kg)/(5.24 × 10ˉ⁴ m³) = 1950 kg/m³, using 3 significant figures.

The density of the aluminium is greater than this, so the block will sink.