Question

A barometer tube reads $75\text{cm}$ of $Hg$. If the tube is gradually inclined at an angle of ${30}^{\circ }$ with the horizontal, keeping the open end in the mercury container, find the length of the mercury column in the barometer tube.

• A. $86.7\text{cm}$
• B. $150\text{cm}$
• C. $75\text{cm}$
• D. $92.5\text{cm}$

Answer 1

The correct option is B $150\text{cm}$

$\because$ We are not changing the atmospheric pressure, so vertical height of $Hg$ from the surface should not change.

That is the horizontal height of $Hg$ = $l=75cm$.


From the above figure, we have

$cos\left(\theta \right)=\frac{l}{x}$

So, $\frac{75}{x}=\cos {60}^{\circ }$
or $x=150\text{cm}$

Thus, the length of the mercury column in the barometer tube is $150cm$.