The height of a mercury barometer is 95 cm at sea level and 60 cm at the top of a hill. The ratio of density of mercury to that of air is 104. The height of the hill is

Question

The height of a mercury barometer is 95 cm at sea level and 60 cm at the top of a hill. The ratio of density of mercury to that of air is 104. The height of the hill is (A) 2 km (B) 3 km (C) 4 km (D) 5 km

Tardigrade Admin · Accepted Answer

Δ h 'P Hg g = h ρ air g h =(Δ h ' ρ Hg g /ρ ar g ) =(95-60) 10-2 × 10+4 h =35 × 102=3500 ≈ 3 km

Q. The height of a mercury barometer is $95 c m$ at sea level and $60 c m$ at the top of a hill. The ratio of density of mercury to that of air is $1 0^{4}$ . The height of the hill is

$2 km$

$3 km$

$4 km$

$5 km$

$Δ h^{'} P_{H g} g = h ρ_{ai r} g$
$h = \frac{Δ h ^{'} ρ _{H g} g}{ρ _{a r} g}$
$= (95 - 60) 1 0^{- 2} \times 1 0^{+ 4}$
$h = 35 \times 1 0^{2} = 3500 \approx 3 km$

Q. The height of a mercury barometer is 95cm at sea level and 60cm at the top of a hill. The ratio of density of mercury to that of air is 104. The height of the hill is

2km

3km

4km

5km