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?

5cm

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10cm

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20cm

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None of the above

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Solution

The correct option is A
5cm

We use the formula P = $ρ g h$

$P_{1}$ = $ρ_{1} g h_{1}$

$P_{2}$ = $ρ_{2} g h_{2}$ where $ρ_{1}$ is the density of A and $ρ_{2}$ is the density of B

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

$ρ_{1} g h_{1}$ = $ρ_{2} g h_{2}$

$ρ_{1} h_{1}$ = $ρ_{2} h_{2}$

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

$2 ρ_{2} h_{1}$ = $ρ_{2} h_{2}$

$2 h_{1}$ = $h_{2}$

Given $h_{2}$ = 10cm.

$h_{1}$ - 5cm

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