oil is added to the right hand arm of a U-tube containing water.The oil floats above the water to a height of h=10cm.The top of the oil+water column is a height d=2cm above the top of the water column in the other arm .Calculate the oil density?

800kg/m^-3

To calculate the density of oil, we need to use the principles of hydrostatics and the equation for pressure difference.

Here's how we can calculate the density of the oil:

1. First, let's identify the given values:
- Height of the oil column (h) = 10 cm
- Height difference between the top of the oil+water column and the top of the water column in the other arm (d) = 2 cm

2. Since the oil floats on water, it implies that the pressure at the same height in both arms is equal. Therefore, the pressure at the top of the oil+water column is the same as the pressure at the top of the water column in the other arm.

3. The pressure at a certain height in 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 fluid column.

4. We can set up two equations for the pressures at the top of the oil+water column and the top of the water column in the other arm:
- P1 = ρ1 * g * (h + d)
- P2 = ρ2 * g * h

5. Since the pressure at both points is the same, we can equate the equations and solve for the density of the oil (ρ1):
- ρ1 * g * (h + d) = ρ2 * g * h

6. Canceling out the common factors and rearranging the equation, we get:
- ρ1 = (ρ2 * h) / (h + d)

7. Now we can substitute the known values:
- ρ2 is the density of water, which is approximately 1000 kg/m³.
- h = 10 cm = 0.1 m
- d = 2 cm = 0.02 m

Substituting these values into the equation, we get:
ρ1 = (1000 kg/m³ * 0.1 m) / (0.1 m + 0.02 m)

8. Evaluating the equation, we find:
ρ1 = 1000 kg/m³ / 1.1 m

9. Therefore, the density of the oil is approximately:
ρ1 = 909.09 kg/m³

So, the density of the oil is approximately 909.09 kg/m³.