(a) Pressure decreases as one ascends the atmosphere. If the density of air is `rho,` What is the change in pressure dp over a differential height dh ? (b) Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the sureface of the earth is `p_0.` (c ) If `p_0 = 1.03 xx 10^5 Nm^(-2), rho_0 = 1.29kg m^(-3) and g = 9.8 ms^(-2), ` at what height will the pressure drop to `(1//10)` the value at the surface of the earth ? (d) This model of the atmosphere works for relatively small distance. Identify the underlying assumption that limits the model.