You enter a competition to design an oil (Poi; : 0.9 g/ml) and vinegar (ppm 2 1.3 g/ml) bottle. You know that oil and vinegar do not mix, so you come up with an amazing ideal Your design consists of an open-ended U-shaped tube, as in the figure above, with an inner diameter of d = 5 cm. The bent part of the tube can hold 300ml of liquid. The straight parts are 15 Cm high. You start by adding a volume V0 of vinegar to the tube, and then add oil until it reaches the top of one end of the tube without overflowing [Recall 1 m1 : 1 Cm3]. (a) Write an expression for hm-n, in terms of hog-g, p011, and pm\". [Hint: Consider the pressure at the position marked by the red dashed line]. (b) Write an expression for the total volume VD of vinegar in terms of hog-g and hm-n. (c) Suppose that Vo = 500 ml. Using your answers from the previous parts, determine the maximum amount of oil (in ml) you can add to one end without the tube overflowing. [Hint: You have two equations and two unknowns]. ml