A manometer tube contains mercury of density `13.6 xx 10^(3)` kg `m^(-3)`. What difference in the levels of mercury in the two arms is indicated by a gauge pressure of `1.03 xx 10^(5) Pa`?

Explanation

To solve the problem, we need to determine the difference in the levels of mercury in the two arms of the manometer due to a given gauge pressure. We can use the relationship between pressure, density, gravitational acceleration, and height difference.

### Step-by-Step Solution:

1. **Identify the given values:**
- Density of mercury, \( \rho = 13.6 \times 10^3 \, \text{kg/m}^3 \)
- Gauge pressure, \( P = 1.03 \times 10^5 \, \text{Pa} \)
- Acceleration due to gravity, \( g \approx 10 \, \text{m/s}^2 \) (for simplicity)
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