Match the following liquids to their corresponding column heights ( $h_{1}, h_{2}, h_{3}$ )
in a barometer. ( $h_{1} > h_{2} > h_{3}$ )

h_{1}

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h_{2}

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h_{3}

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Solution

We know that the liquid in the column balances the atmospheric pressure ( $P_{a t m}$ ) in the barometer.

$P_{a t m} = ρ g h$
$ρ =$ Density of liquid
$g =$ Gravitational acceleration
$h =$ Height of the column

The height of the column will increase as the density of the liquid decreases.
Increasing order of the density is:
Oil > Water > Mercury.
Hence, increasing order of water column is:
Mercury > Water > Oil
As a result, the height of the column for water, oil and mercury will be $h_{2}, h_{1} and h_{3}$ respectively.

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