A) 1.25 km
B) 2.5 km
C) 250 m
D) 750 m
Correct Answer: B
Solution :
Pressure differences 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 metre of air \[\Delta p=h\times {{\rho }_{air}}\times g\] ?(ii) By equating Eqs. (i) and (ii) \[h\times {{\rho }_{air}}\times g\] \[=(75-50)\times {{10}^{-2}}\times {{\rho }_{Hg}}\times \rho \] \[h=25\times {{10}^{-2}}\left( \frac{{{\rho }_{Hg}}}{{{\rho }_{air}}} \right)\] \[=25\times {{10}^{-2}}\times {{10}^{4}}\] \[=2500\,m\] \[\therefore \]Height of hill \[=2.5\,km\]
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