JEE Advanced Physics: Fluid Mechanics / Geometry of flux questions with solutions

Q1. A cylindrical container of base area A has its top opening of area A1 cut at an angle of 30 degrees to the horizontal (a slanted mouth). It is placed in steady vertical rain next to a second cylindrical container that has the same base area A but a horizontal top opening. Find the ratio of the rates at which the two containers collect rainwater.

1. 1: 1
2. 1: 2
3. 2: 1
4. 1: sqrt(3)

Answer: 1: 1

Rain falls vertically, so the rate of water collection depends only on the horizontal projected area of the opening. The slanted opening of the first cylinder projects onto a horizontal circle of area A (the base area), and the second container also has horizontal opening area A. Therefore both collect rain at the same rate, giving a ratio 1: 1.