Determine the ratio of the weights of a 1 kg block of iron and a 1 kg block of wood, as measured by a spring balance. The density of iron is 7800 kg m ⁻³ , the density of wood is 800 kg m ⁻³ , and the density of air is 1.293 kg m ⁻³ .

Step-by-step solution

The spring balance measures the apparent weight of an object, which is its true weight minus the buoyant force exerted by the displaced air. The apparent weight W of a block of mass m and density is given by: W = mg - F_ b = mg - V _ air g = mg ( 1 - _ air ) For the iron block, the apparent weight is: W_ iron = mg ( 1 - _ air _ iron ) For the wood block, the apparent weight is: W_ wood = mg ( 1 - _ air _ wood ) The ratio of their weights as measured by the spring balance is: W_ iron W_ wood = 1 - _ air _ iron 1 - _