Question

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Answer 1

Hydrostatic Pressure of a Liquid Column

• The pressure exerted by a liquid in a column at the base depends only on the height of the liquid in the column.

• It does not depend on the cross-sectional area or the shape of the column. Just the Height.

• This Hydrostatic Pressure of a liquid of density $\rho$ with a height $h$ in a column is given by:

$\large\boxed{P = \rho gh}$

Here, $g$ is the acceleration due to gravity.

$\rule{300}{1}$

• Here, in the Question, we have two liquids: Mercury and Water. They are in two different columns. We need the height of the water in its column.

• The Pressure exerted by both liquids at the base is the same. So, we can equate them to find height of water in the column.

Mercury

• $\rho_1 = 13.6\ g/cm^3 \\ \\ h_1 = 70\ cm$

Water

• $\rho_2 = 1\ g/cm^3 \\ \\ h_2 = ?\ cm$

Equating the Pressures, we have:

$P_1 = P_2 \\\\\\ \implies \rho_1 \cancel{g} h_1 = \rho_2 \cancel{g}h_2 \\\\\\ \implies 13.6 \times 70 = 1 \times h_2 \\\\\\ \implies h_2 = 13.6\times 70\ cm \\\\\\ \implies \Large\boxed{\bold{h_2 = 952\ cm}}$

•Thus, The Height of the Water Column is 952 cm.

Answer 2

Answer:

Pressure at the place remains the same for both water and mercury.

Pressure exerted by mercury = density of mercury * height of mercury column * g (acc. due to gravity)

=> Pressure exerted by mercury = 13.6 * 70 * g

=> Pressure exerted by mercury = 952 g.

Pressure exerted by water = density of water * height of water column * g (acc. due to gravity)

=> Pressure exerted by water = 1 * h *g

=> Pressure exerted by water = h g.

Now, According to question,

952* g = h* g

=> h = 952 cm.

Therefore, the height of water column which will exert on its base the same pressure as the 70 cm column of mercury is 952 cm.

hope this helps you