The U-tube in Fig contains two liquids in static equilibrium : Water of density `rho_(w) = (998 kg//m^(3)`) is in the right arm , and oil of unknown density `rho` , is in the left . Measurement gives l = 135 mm and d = 12.3 mm .what is the density of the oil ?

Explanation

To find the density of the oil in the U-tube, we can use the principle of hydrostatic equilibrium. The pressures at the same horizontal level in both arms of the U-tube must be equal.

### Step-by-step Solution:

1. **Identify the given values:**
- Density of water, \( \rho_w = 998 \, \text{kg/m}^3 \)
- Length of water column, \( L = 135 \, \text{mm} = 0.135 \, \text{m} \)
- Length of oil column, \( d = 12.3 \, \text{mm} = 0.0123 \, \text{m} \)
...