A sphere made of a material with density 12 kg m ⁻³ and weighing 100 N in vacuum is immersed in a container of gas. Its weight in gas is 85 N. The density of the gas in kg m ⁻³ is closest to

Step-by-step solution

Weight of the sphere in vacuum is given by W = V _s g = 100 N. Apparent weight of the sphere in the gas is W' = W - F_B = 85 N. The buoyant force exerted by the gas is F_B = V _g g = 100 - 85 = 15 N. Taking the ratio of the buoyant force to the true weight: V _g g V _s g = 15 100 _g _s = 0.15 Substituting the density of the sphere _s = 12 kg m ⁻³ : _g = 0.15 12 = 1.80 kg m ⁻³ Answer: 1.80