Question

A barometer reads $76\text{cm}$ of mercury. If the tube is gradually inclined at an angle of ${45}^{\circ }$ with the vertical, keeping the open end immersed in the reservoir, then the length of the mercury column will be -

• A. $86\text{cm}$
• B. $76\text{cm}$
• C. $76\sqrt{2}\text{cm}$
• D. $100\text{cm}$

Answer 1

The correct option is C $76\sqrt{2}\text{cm}$

Let us suppose $P_0$ is the atmospheric pressure and $P_1$ is the pressure inside the tube at the level of the water outside the tube.
Figure as per question -



We know that, pressure at all points in a horizontal plane in a static fluid is equal.
$\therefore P_0=P_1=76\text{cm}$ of Hg
[ for initial case ]
and ${\rho }_{m}gh=P_0-0=P_0$
[ because top of the tube is vacuum]
Atmospheric pressure will not change if the tube is inclined with the vertical.
Therefore, after the inclination of the tube, vertical height of the mercury in the tube ($h$) will be the same as in initial case i.e $76\text{cm}$
$\Rightarrow h=76\text{cm}$
[ from the final case figure ]
$\Rightarrow L\cos {45}^{\circ }=76$
$\Rightarrow L=76\sqrt{2}\text{cm}$