In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respect

Question

In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height of the water and oil columns are 15 cm and 20 cm respectively. The density of the oil is: [take ρ_water = 1000 kg/m^3]

Accepted Answer

1. **Principle:** According to Pascal's Law and the principles of hydrostatics, the pressure at the same horizontal level in a continuous liquid at rest is the same . In a U-tube, the pressure exerted by the liquid columns at the level of the interface must be equal.
2. **Formula:** The pressure exerted by a liquid column is given by $P = ho g h$, where $ho$ is density, $g$ is acceleration due to gravity, and $h$ is the height of the column .
3. **Calculation:** Equating the pressure exerted by the water column to that of the oil column:
   $$ ho_{water} g h_{water} = ho_{oil} g h_{oil} $$
   $$ 1000 	imes g 	imes 15 = ho_{oil} 	imes g 	imes 20 $$
   Canceling $g$ from both sides:
   $$ 15000 = 20 ho_{oil} $$
   $$ ho_{oil} = \frac{15000}{20} = 750 	ext{ kg/m}^3 $$

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