Question

The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is 104. The height of the hill is

• A. 250 m
• B. 2.5 km
• C. 1.25 km
• D. 750 m

Answer 1

The correct option is B

2.5 km

Difference of pressure between sea level and the top of hill $\Delta p=(h_1-h_2)\times P_{Hg}\times g=(75-50)\times {10}^{-2}\times p_{Hg}\times g.....\left(i\right)$ and pressure difference due to h meter of air $\Delta P=h\times p_{air}\times g.....\left(ii\right)$ By equating (i) and (ii) we get $h\times P_{air}\times g=(75-50)\times {10}^{-2}{P}_{Hg}\times g$ $\therefore h=25\times {10}^{-2}\times {10}^{-4}=2500m$ $\therefore$ Height of the hill = 2.5 km.