Pressure Problem

Classical Mechanics Level 2

The height of Hg barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of Hg to that of air is 1 0 4 10^{4} .The height of the hill (in metres) is:

1250 2500 250 750

Anik Mandal by Anik Mandal , 21, India

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2 solutions

Lu Chee Ket
Oct 7, 2015

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 m for Hg: 13600 km/ m^3

0 m for air: 1.2 kg/ m^3

1000 m for air: 1.1 kg/ m^3

5000 m for air : 0.7 kg/ m^3

10^4 is a good approximation to 13600/ 1.2 as a ratio.

76 cm Hg instead of 75 cm Hg is more commonly known at certain conditions.

Lu Chee Ket - 5 years, 8 months ago
Chew-Seong Cheong
Sep 13, 2015

Assuming constant air density ρ a i r = 1 0 − 4 ρ H g \rho_{air} = 10^{-4}\rho_{Hg} in the atmosphere. Let the thickness of atmosphere be H H . Then at sea level, ρ a i r g H = ρ H g g h H g \rho_{air}gH = \rho_{Hg}gh_{Hg} , where g g is acceleration due to gravity. Therefore, H = 1 0 4 × 75 × 1 0 − 2 = 7500 H =10^{4} \times 75 \times 10^{-2} = 7500 m.

Now, let the height of the hill be h h , then: ρ a i r g ( H − h ) = ρ H g g h H g ′ \rho_{air}g(H-h) = \rho_{Hg}gh_{Hg}' . Therefore, H − h = 1 0 4 × 50 × 1 0 − 2 = 5000 H-h = 10^{4} \times 50 \times 10^{-2} = 5000 m. ⇒ h = H − 5000 = 7500 − 5000 = 2500 \Rightarrow h = H - 5000 = 7500 - 5000 = \boxed{2500} m.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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