Question

the ratio of height of mercury column in a barometer at a given place to height of the liquid column at a same place are 1 : 4 find the density of the liquid

Answer 1

Answer: $3.4 g/cm^3$

Explanation:

we know that pressure is related to density as:

P=hρg

where, h is the height, ρ is the density and g is acceleration due to gravity.

At a same place, the pressure experience would be same.

$P_Hg=P_l$

The density of mercury $\rho_1=13.56 g/cm^3$

The ratio of height of mercury column to liquid column is $h_1:h_2 = 1:4.$

$h_1\rho_1g=h_2\rho_2g\\ \Rightarrow \frac{h_1}{h_2}=\frac{\rho_2}{\rho_1}\\ \Rightarrow \frac{1}{4}=\frac{\rho_2}{13.56 g/cm^3}\Rightarrow \rho_2= \frac{13.56 g/cm^3}{4}= 3.4 g/cm^3$

Hence, the density of the liquid $3.4 g/cm^3$