A spring balance measures the weight of an empty balloon to be W₁ . After filling the balloon with air, its weight becomes W₂ . Let w denote the weight of the air itself. Disregard the thickness of the inflated balloon. Furthermore, ignore any difference between the densities of the air inside and outside the balloon.

Step-by-step solution

Let the true weight of the empty balloon material be W₀ and its volume be v . The buoyant force acting on the empty balloon due to the surrounding air is F_ b1 = _ air v g . The spring balance measures the apparent weight. Thus, the apparent weight of the empty balloon is: W₁ = W₀ - _ air v g When the balloon is inflated, let the volume of the air inside be V . The true weight of the air inside is given as w , so w = _ air V g (since the densities of air inside and outside are the same). The total true weight of th