The density of asir ner earth's surface is `1.3kgm^-3` and the atmospheric pressure is `1.0xx10^5Nm^-2`. If the atmosphere had uniform density, same as that observed at the surface of the earth what would be the height of the atmosphere to exert the same pressure?

Explanation

To solve the problem, we need to find the height of the atmosphere that would exert the same pressure as given, assuming a uniform density of air equal to that at the surface of the Earth.

### Step-by-Step Solution:

1. **Identify the given values**:
- Density of air, \( \rho = 1.3 \, \text{kg/m}^3 \)
- Atmospheric pressure, \( P = 1.0 \times 10^5 \, \text{N/m}^2 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
...