Question

The ratio of height of a mercury column in a barometer at a place to the height of the liquid column at the same place are $1:4$. Find the density of the liquid

Answer 1

Let the density of liquid be ${\rho }_l$ and mercury be ${\rho }_m$.

Now as given let the mercury rises to H height and liquid rises to 4H height .

So at the bottom pressure must be same.

As we know pressure $P=\rho gH$

By pascal's law , pressure is same on any point at the same horizontal level.

So ${\rho }_{m}gH=\rho g4H$

on solving above equation

${\rho }_l={\rho }_m/4$

as we know the density of mercury is $13.6g/c{m}^3$

So ${\rho }_l=\frac{13.6}{4}=3.4g/c{m}^3$