Question

To construct a barometer, a tube of length 1 m is filled completely with mercury and is inverted in a mercury cup. The barometer reading on a particular day is 76 cm. Suppose a 1 m tube is filled with mercury up to 76 cm and then closed by a cork. It is inverted in a mercury cup and the cork is removed. The height of mercury column in the tube over the surface in the cup will be
(a) zero
(b) 76 cm
(c) > 76 cm
(d) < 76 cm

Answer 1

(d) < 76 cm

Because of the trapped air, the pressure at the upper end of the mercury column inside the tube is not zero.
In other words, ${\mathrm{P}}_0>0$.
Using this relation, we get:
$$\begin{gathered} P_{\mathrm{atm}}=P_0+\mathrm{\rho }gh \\ \mathrm{Here}, \\ \mathrm{\rho }=\mathrm{Density}\mathrm{of}\mathrm{mercury} \\ h=\mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{mercury}\mathrm{column} \\ \because P_0>0 \\ \mathrm{And}, \\ {P}_{\mathrm{atm}}>\mathrm{\rho }gh \\ \therefore 76\mathrm{cm}\mathrm{of}\mathrm{Hg}>\mathrm{\rho }gh \\ \mathrm{or},h<76\mathrm{cm} \end{gathered}$$