Question

Liquid A and liquid B extrat same amount of pressure on each other but density of A is twice density of B height if liquid B is 10 cn then height of liquid A would be 1 point

Answer 1

Answer:

Given:

Liquid A and liquid B exert same pressure at the bottom of a container. But Density of A is twice the density of B. Height of B column is 10 cm.

To find:

Height of A column

Calculation:

We know that liquid columns exert pressure at the bottom of a container following the relationship as follows :

$\boxed{ \bold{P = \rho \times g \times h}}$

For liquid A , we say :

$P_{A} = \rho_{A} \times g \times h_{A}$

For liquid B , we say :

$P_{B} = \rho_{B} \times g \times h_{B}$

Dividing the 2 Equations, we get :

$1 = \dfrac{\rho_{A}}{\rho_{B}} \times \dfrac{h_{A}}{h_{B}}$

$= > h_{B} = 2 \times h_{A}$

$= > h_{A} = \dfrac{h_{B}}{2} = 5 \: cm$

So final answer is h(B) is 5 cm

Answer 2

AnswEr :

Given :

• The liquids exert equal pressure on eachother

• Density of Liquid A is twice of Density of Liquid B

• Both are the liquids are 10 cm apart

Explanation :

Pressure exerted by a liquid w.r.t to height is given by :

$\sf \: p_{atm} = p_o + \rho gh \: \\ \\ \longrightarrow \: \sf \: p_a - p_o = \rho gh \\ \\ \longrightarrow \boxed{ \boxed{ \sf P_T = \rho \times g \times h}}$

For Liquid A :

$\sf \: P_a = 2\rho gh - - - - - - - (1)$

For Liquid B :

$\sf \: P_b = \rho gh - - - - - - - - (2)$

Dividing both the equations,we get :

$\implies \sf \cancel{\dfrac{P_a}{P_b}} = \dfrac{2 \times h}{10} \times \cancel{ \dfrac{ \rho \: g}{ \rho \: g}} \\ \\ \implies \: \sf \: h = \dfrac{10}{2} \\ \\ \implies \: \boxed{ \boxed{ \sf h = 5 \: cm}}$

Height of Liquid A is 5 cm