The height of mercury barometer is 75 cm at sea level and 50 cm at top of a hill. Ratio of density of mercury to that of air is 10 4 . the height of the hill is

Step-by-step solution

Difference of pressure between sea level and the top of the hill Δ P = h 1 - h 2 × ρ Hg × g = 75 - 50 × 10 - 2 × ρ Hg × g .......(i) and pressure difference due to h metres of air ΔP = h × ρ air × g ......(ii) By equating (i) and (ii) we get h × ρ air × g = ( 75 - 50 ) × 10 - 2 × ρ Hg × g ∴ h = 25 × 10 - 2 ρ Hg ρ air = 25 × 10 - 2 × 10 4 = 2500 m ∴Height of the hill =   2 . 5 &#1