Question

A faulty barometer shows 72 cm and the air column is 10 cm, when the true atmospheric pressure is 76 cm of Hg. The barometer reading will be, when the length of the air column is 5 cm (in cm of Hg)

Answer 1

Given:

A faulty barometer shows 72 cm and the air column is 10 cm, when the true atmospheric pressure is 76 cm of Hg.

To find:

Reading of barometer when the length of air column is 5 cm.

Calculation:

As per faulty reading of the barometer :

$\boxed{ \red{\rm{air \: pressure \: \propto \: h} }}$

In 1st case :

$\sf {\therefore \: ( \rho \times g \times 10 )\: \propto \: 72 \: cm}$

In 2nd case ; let height of mercury be h ;

$\sf {\therefore \: ( \rho \times g \times 5)\: \propto \: h \: cm}$

Taking ratio on both sides :

$\sf{ \therefore \: \dfrac{ \rho \times g \times 10}{ \rho \times g \times 5} = \dfrac{72}{h} }$

$\sf{ = > \: \dfrac{ \cancel{\rho \times g} \times 10}{ \cancel{ \rho \times g }\times 5} = \dfrac{72}{h} }$

$\sf{ = > \: \dfrac{ 10}{ 5} = \dfrac{72}{h} }$

$\sf{ = > \: 2 = \dfrac{72}{h} }$

$\sf{ = > \: h = \dfrac{72}{2} }$

$\sf{ = > \: h = 36 \: cm}$

So , final answer is :

Height of mercury column is 36 cm