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

Q: 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 $10^4$. The height of the hill is ....... $km$

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

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

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 $10^4$. The height of the hill is ....... $km$

A$25 $
B$2.5 $
C$1.25$
D$75$

Diffcult

STD 11 Science
NEET
STD 11 - 9.1. fluid mechanics
Physics

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