It is given that both liquid A and liquid B exert the same amount of pressure on their respective bases. The density of liquid A is twice the density of liquid B. The height of the column of liquid B is $10 c m$ . What would be the height of the column of liquid A?

5 c m

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15 c m

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20 c m

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10 c m

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Solution

The correct option is A $5 c m$
A liquid column with depth $h$ , applies a pressure:
$P = ρ g h$
where:
$ρ -$ Density
$g -$ Acceleration due to gravity

Using this,
Pressure in liquid A, $P_{A} = ρ_{A} g h_{A}$
Pressure in liquid B, $P_{B} = ρ_{B} g h_{B}$

It is given that the pressures are equal.
$P_{A} = P_{B}$
$ρ_{A} g h_{A} = ρ_{B} g h_{B}$
$ρ_{A} h_{A} = ρ_{B} h_{B}$

It is given that the density of liquid A is twice the density of liquid B.
$ρ_{A} = 2 (ρ_{B})$
Substituting this, we get:
$2 ρ_{B} h_{A} = ρ_{B} h_{B}$
$2 h_{A} = h_{B}$

It is given that the height of liquid B is 10 cm.
$h_{B} = 10 c m$
So, $h_{A} = 5 c m$

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It is given that both liquid A and liquid B exert the same amount of pressure on their respective bases. The density of liquid A is twice the density of liquid B. The height of the column of liquid B is 10 cm. What would be the height of the column of liquid A?

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