A) 250 m
B) 2.5 km
C) 1.25 km
D) 750 m
Correct Answer: B
Solution :
Difference of pressure between sea level and the top of hill DP\[=({{h}_{1}}-{{h}_{2}})\times {{\rho }_{Hg}}\times g\]\[=(75-50)\times {{10}^{-2}}\times {{\rho }_{Hg}}\times g\] ?(i) and pressure difference due to h meter of air DP =\[h\times {{\rho }_{air}}\times g\] ?(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.
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