Question

The atmospheric pressures at the top and the bottom of a building are read by a barometer to be 96.0 and 98.0 kPa. If the density of air is 1.0 kg/m^3, the height of the building is (a) 17 m (b) 20 m (c) 170 m (d) 204 m (e) 252 m e

Answer 1

Answer:

Option d - 204 m

Step-by-step explanation:

Given : The atmospheric pressures at the top and the bottom of a building are read by a barometer to be 96.0 and 98.0 kPa. If the density of air is 1.0 kg/m³.

To find : The height of the building ?

Solution :

We have given atmospheric pressures,

$P_{\text{top}}=96\ kPa$

$P_{\text{bottom}}=98\ kPa$

The density of air is 1.0 kg/m³ i.e. $\rho_a=1\ kg/m^3$

Atmospheric pressure reduces with altitude,

The height of the building is given by formula,

$H=\frac{\triangle P}{\rho_a\times g}$

$H=\frac{P_{\text{bottom}}-P_{\text{top}}}{\rho_a\times g}$

$H=\frac{(98-96)\times 10^3}{1\times 9.8}$

$H=\frac{2000}{9.8}$

$H=204\ m$

Therefore, Option d is correct.

The height of the building is 204 meter.