Question

The liquids shown in the figure in the two arms are mercury (specific gravity = 13.6) and water. if the difference of heights of the mercury columns is 2 cm, find the height h of the water column. Acceleration due to gravity $g=10m/s^2$

• A. 0.27 cm
• B. 27 cm
• C. 2 mm
• D. 27 dm

Answer 1

The correct option is B

27 cm

Suppose the atmospheric pressure = $P_0$

Pressure at A = $P_0+h\left(1000kg{m}^{-3}\right)g$

Pressure at B = $P_0+\left(0.02m\right)\left(13600kg{m}^{-3}\right)g$

These pressures are equal as A and B are at the same horizontal level.

$P_0+h\left(1000kg{m}^{-3}\right)g$ = $P_0+\left(0.02m\right)\left(13600kg{m}^{-3}\right)g$
$h$ = $0.02\times 13.6$

=$0.27m=27cm$