Question

The height of a mercury barometer is $75cm$ at sea level and $50cm$ at the top of a hill a. Ratio of density of mercury to that of air is ${10}^4$ .The height of the hill is:

• A. $1.25km$
• B. $2.5km$
• C. $250m$
• D. $750m$

Answer 1

Answer: (B)

$2.5km$

Pressure differences between sea level and the top of hill
$△p=(h_1-h_2)\times p_{Hg}\times g$
$=(75-50)\times {10}^{-2}\times p_{Hg}\times g$ ...(i)
and pressure difference due to h metre of air
$△p=h\times p_{air}\times g$ ...(ii)
By equating Eqs. (i) and (ii)
$h\times p_{air}\times g$
$=(75-50)\times {10}^{-2}\times p_{Hg}\times p$
$p=25\times {10}^{-2}\left(\frac{p_{Hg}}{p_{air}}\right)$
$=25\times {10}^{-2}\times {10}^4=2500m$
$\therefore$ Height of hill = 2.5 km