Two students are each given a spherical balloon that has a long string attached and is filled with an unknown gas whose density is referred to by the variable PG. The filled balloons each have a radius referred to by the variable R and a volume referred to by the variable V, and the balloons rise when released. A small valve is fitted to each balloon to allow the balloon to be deflated in a controlled manner. (a) The string and the balloon itself (not including the gas) have a combined known mass of MB. Derive an expression for the acceleration of the balloon when it is released in terms of the given quantities and physical constants, as appropriate. Air resistance is negligible, and the known density of air is PA- (b) The first student is given a stopwatch and a tape measure and asked to use only this equipment in an experiment to determine the density of the gas inside the balloon from a graph of the data. Describe an experimental procedure the student can use to accomplish this. 1.2+ 1.0+ 0.8+ Z -0.6- 0.4+ 0.2+ 0.05 0.10 0.15 -0.2+ -0.4+ Volume (m) (c) The second student is given a force sensor, and the student attaches it to the balloon's string. The balloon's volume and the force required to keep the balloon at rest are measured. The valve is opened, releasing some gas from the balloon, and the measurements are repeated. The graph shows the data obtained. Describe how the graph could be used to determine the mass of the balloon and the density of the gas. Force (N)