Please reference the following picture for this question:
screenshots<dot>firefox<dot>com/V57wh6MYWUXfnx5M/brilliant<dot>org
Initially, the U-tube shown above is filled with water, and the level on each side is l0. After some oil is poured on side A, the level on that side becomes La=7.3cm
What is Lb (in cm)?
Assume that the water and oil do not mix, and that their densities are related by P_oil=0.85 P_water
To find the level Lb (in cm) on side B, we can use the concept of pressure. The pressure at any point in a fluid is given by the equation:
Pressure = density * gravitational acceleration * height
Since both sides are in equilibrium, the pressure on both sides should be equal:
Pressure on side A = Pressure on side B
We can relate the pressures by their heights:
density_water * gravitational acceleration * l0 = density_oil * gravitational acceleration * La + density_water * gravitational acceleration * Lb
Now, we can substitute the given relationship between the densities of oil and water:
P_oil = 0.85 * P_water
density_water * gravitational acceleration * l0 = 0.85 * density_water * gravitational acceleration * La + density_water * gravitational acceleration * Lb
Simplifying the equation:
l0 = 0.85 * La + Lb
Now, we can substitute the given values:
l0 = 0.85 * 7.3 + Lb
l0 = 6.205 + Lb
Subtracting Lb from both sides:
l0 - Lb = 6.205
Finally, we can solve for Lb:
Lb = l0 - 6.205
Now, referring to the provided picture, you can determine the value of l0 (initial level) and calculate Lb using the equation above.