please answer all parts clear and full

In this question you will consider how a spherical soap bubble of radius r floating in the air shrinks over time (assume it stays floating and does not burst). The soap film has a surface tension (dimensions of force over distance). (a) Using dimensional analysis, show that the excess pressure inside the bubble is given by P=cr where c is a dimensionless constant, and P is the difference between the air pressure inside and outside the bubble. [4 marks] (b) Given that P1 bar, sketch how you expect the bubble's size to vary over time, assuming the air inside the bubble diffuses through the soap film at a rate proportional to the excess pressure. [4 marks] (c) With this assumption from part (b), show that the variation of the bubble radius with time is described by dtdr=rD where D is an appropriate parameter. What is the value of ? [6 marks] (d) Solve this equation to derive an expression for r(t); how long is it until the bubble shrinks to size zero in terms of the parameters? [6 marks]