a u-tube is partially filled with water.oil which does not mix with water is next poured into one side until water rises by 2.5cm on the other side.if the density of oil be 0.8 ,the oil level will stand higher than the water level by how much?
ans is 12.50
To find out how much higher the oil level will stand compared to the water level, we can use the concept of density and the hydrostatic pressure formula.
First, let's define the variables:
Hw = Height of water column
Ho = Height of oil column
ρw = Density of water
ρo = Density of oil
In this case, we know that the water level rises by 2.5 cm, so Hw = 2.5 cm.
The hydrostatic pressure exerted by a fluid column is given by the equation P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height of the column.
Since the pressure at the interface between the water and oil must be equal, we can equate the pressures:
ρw * g * Hw = ρo * g * Ho
Since g is the same for both sides, we can cancel it out:
ρw * Hw = ρo * Ho
Now we can rearrange the equation to solve for Ho:
Ho = (ρw * Hw) / ρo
Given that the density of oil (ρo) is 0.8 and the height of the water column (Hw) is 2.5 cm, we can substitute these values into the equation:
Ho = (ρw * Hw) / ρo = (1 * 2.5) / 0.8 = 3.125 cm
Therefore, the oil level will stand higher than the water level by 3.125 cm.