A simple U-tube contains mercury. When 11.2 cm of water is poured into the right ann, how high does the mercury rise in the left arm from its initial level ?

When 11.2 cm of water is poured into the right arm of a simple U-tube containing mercury, the mercury will rise in the left arm. To find out how high the mercury rises in the left arm, we can use the concept of pressure and the properties of fluids.

Understanding Pressure in a U-tube

In a U-tube, the pressure at any point in a fluid is the same horizontally. This means that the pressure at the same height on both sides of the U-tube is equal.

Solving for the Height of Mercury

When the water is poured into the right arm, the pressure at the same height in both arms must be equal. We can use the following formula to calculate the height of the mercury in the left arm:

P_water = P_mercury

Since pressure is given by the formula P = ρgh (where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height), we can set up the equation as follows:

ρ_waterg(11.2) = ρ_mercuryg(h)

h = (ρ_water/ρ_mercury) * 11.2

Calculating the Height

Mercury is much denser than water, so the density of mercury (ρ_mercury) is greater than the density of water (ρ_water). Therefore, the height of the mercury in the left arm will be less than 11.2 cm.

By substituting the values for the densities of water and mercury (ρ_water = 1000 kg/m³, ρ_mercury = 13600 kg/m³) into the equation, we can calculate the height at which the mercury rises in the left arm.

Conclusion

By solving the equation, you can find out how high the mercury rises in the left arm of the U-tube when 11.2 cm of water is poured into the right arm. This demonstrates the principles of fluid pressure and density in action.