Question

A barometer reads 75 cm of Hg. When 2cc of air at atmpospheric pressure is introduced into the space above the mercury level, the volume of this space becomes 50 cc. The length by which the mercury column descends is

• A. 3 cm
• B. 6 cm
• C. 1.5 cm
• D. 25 cm

Answer 1

The correct option is A 3 cm

initially barometer reads 75 cm ,
so atmosphere pressure $P_a=\rho g\left(0.75\right)$
gas is added at atmosphere pressure, with initial volume 2cc
later volume expands to 50cc.
This is isothermal process,
by boyle's law $P_2{V}_2=P_1{V}_1$
$P_2=\frac{P_1{V}_1}{V_2}$
since $P_1=P_a$
$P_2=\frac{\rho g\left(0.75\right)\times 2}{50}$
$P_2=\rho g\left(0.03\right)$
applying hydro-static pressure equation(as shown in image)
$P_2+\rho gh=P_a$
$\rho g\left(0.03\right)+\rho gh=\rho g\left(0.75\right)$
$h=0.72m=72cm$
descend in mercury column is = $75-72=3cm$

answer is A.