Finding levels of oil-water and oil-air mixed in a tube given specific gravity and distance?

Question

A U-tube is filled with water until the liquid level is 26 cm above the bottom of the tube. An oil of specific gravity 0.72 is now poured into one arm of the U-tube until the level of the water in the other arm of the tube is 31 cm above the bottom of the tube. Find the level of the oil-water and oil-air interfaces in the other arm of the tube.

______cm (oil-water)

______cm (oil-air)

Answer 1

Just to let you know I haven't done this before but I'm pretty sure I can answer this.

I'm taking gravity to be the ratio of density as compared to water, which has a gravity of 1

water went up by 5cm, so this means that a weight equal to10cm worth of water was added to the other side.

as water doesn't really compress the water level on the other side of the arm must have dropped by 5cm, to counter the rise on the opposite side, this means its level is 26-5cm 21cm above the bottom. this is the water oil interface

as the weight of 10cm worth of water must have been added, and the oil is 0.72 the density of the water there must have been 10/0.72 = 13.888cm of oil added so the level of oil is 21+13.88 = 34.88cm above the bottom. this is the oil air interface.