Question

A barometer tube reads 76 cm of mercury. If the tube is gradually inclined keeping the open end immersed in the mercury reservoir, will the length of mercury column be 76 cm, more than 76 cm or less than 76 cm?

Answer 1

The length of the mercury column will be more than 76 cm. The pressure depends on the height of the highest point of the mercury from the ground and not on the length of the liquid column.

$$\begin{gathered} \mathrm{Let}: \\ l=\mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{mercury}\mathrm{column} \\ \theta =\mathrm{Angle}\mathrm{at}\mathrm{which}\mathrm{the}\mathrm{tube}\mathrm{is}\mathrm{inclined}\mathrm{with}\mathrm{the}\mathrm{vertical} \\ \mathrm{Given}: \\ h=76\mathrm{cm} \\ l\cos \theta =h \\ \mathrm{or},l=\frac{h}{\cos \theta } \\ \therefore l>h \end{gathered}$$
Or,
l > 76 cm