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Q.

If water is used in a barometer instead of mercury, what will be the height of the water column for standard atmospheric pressure?

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a

7.6 m

b

10.3 m

c

13.6 m

d

8.6 m

answer is B.

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Detailed Solution

If water is used in a barometer instead of mercury, it will support a water column of height

10.3 m

.
If we use water instead of mercury in a barometer, pressure is the same for both water and mercury, but the heights of the liquid would be different since the densities of both liquids are different. We know that pressure is represented as pressure

= hρg

. If we use water instead of mercury, then,
Equating the pressure exerted by both the liquids as standard atmospheric pressure.

h_{m} ρ_{m} g = h_{w} ρ_{w} g

hρg = pressure

h_{m} =

height of mercury column,

h_{w} =

height of water column

ρ_{m} =

density of mercury (

13.6 gm / cc

)

ρ_{w} =

density of water (

1 gm / cc

)

g =

acceleration due to gravity (

9.81 m / s^{2}

)
Here the height of mercury column

{(h}_{m})

is taken as

76 cm

for the standard atmospheric pressure.

h_{w} ρ_{w} g = 76 \times 13.6 \times 9.81

\Rightarrow

h_{w} = \frac{76 \times 13.6 \times 9.81}{ρ_{w} \times g}

\Rightarrow

h_{w} = \frac{76 \times 13.6 \times 9.81}{1 \times 9.81}

(as the density of water is

1 gm / cc

)

\Rightarrow

h_{w} = 1033.6 cm

\Rightarrow

h_{w} = \frac{1033.6}{100} m

\Rightarrow

h_{w} = 10.3 m

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