Question

It is given that both liquid A and liquid B exert the same amount of pressure. The density of liquid A is twice the density of liquid B. The height of the column of liquid B is 10 cm. Then what would be the height of the column of liquid A?(Use the formula for Pressure(P) as P = $\rho gh$; ${}^{\prime }{\rho }^{\prime }$ is the density of the liquid, 'g' -acceleration due to gravity, 'h'- height of the liquid column)

• A. 20 cm
• B. 15 cm
• C. 10 cm
• D. 5 cm

Answer 1

The correct option is D

5 cm

We use the formula P = $\rho gh$

$P_1$ = ${\rho }_{1}g{h}_1$

$P_2$ = ${\rho }_{2}g{h}_2$ where ${\rho }_1$ is the density of A and ${\rho }_2$ is the density of B

Given that the pressures are equal, we can equate both the equations.

${\rho }_{1}g{h}_1$ = ${\rho }_{2}g{h}_2$

${\rho }_1{h}_1$ = ${\rho }_2{h}_2$

The density of liquid A is twice the density of liquid B

$2{\rho }_2{h}_1$ = ${\rho }_2{h}_2$

$2h_1$ = $h_2$

Given $h_2$ = 10 cm.

$h_1$ = 5 cm