Question

The velocity of sound in air at room temperature is $340\text{m/s}$ and density of air is $1.2{\text{kgm}}^{-1}$. The value of atmospheric pressure in terms of the height of mercury column in metre will be

• A. $0.75$
• B. $7.5$
• C. $75$
• D. $750$

Answer 1

Answer: (A)

$0.75$

${\rho }_{air}=1.2kg{m}^{-3}$

$V_s=\sqrt{\frac{\gamma p}{\rho }}$
$340=\sqrt{\frac{1.4\times p}{1.2}}$

$p=\frac{{340}^2\times 1.2}{1.4}=99086{\text{Nm}}^{-2}$

$p=h{\rho }_{Hg}g$
$h=\frac{99086}{{\rho }_{Hg}g}$
${\rho }_{Hg}=13594{\text{kgm}}^{-3}$

$h=\frac{99086}{13594\times 9.8}=0.743\text{m}$

Option 'A' is correct.