Question

If the mercury in the barometer is replaced by water, What will be the resulting height of the water column? Given: Density of water = 1000 kgm3, Density of mercury = 13600 kgm3

A
0.76 m
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B
10.3 m
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C
11.2 m
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D
9.8 m
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Solution

The correct option is A 10.3 m Height of mercury column = 76 cm Height of water column = h cm We know, Pressure for a height 'h' = ρgh Since, pressure need to equal so, Pressure for mercury column = Pressure for water column ρHg×g×76cm = ρWatergh By putting all the values, 13600×g×76 = 1000g×h On solving, h=1033.6 cm = 10.3 m Theory: Mercury Barometer: Measures atmospheric pressure by determining the height of a mercury column supported in a sealed glass tube. Consider a half filled glass with liquid. Put the straw in the glass. Suck a small amount of liquid into the straw. Hold your finger across the top of the straw. Take the straw out of the liquid, it is observed that the liquid level will not fall. When we let go, the finger across the liquid level falls quickly down. This is because of the pressure differences. Liquid doesn’t fall from the inverted because the upwards force exerted by the atmosphere is stronger than the force of gravity pulling down on the liquid. A cylindrical glass has circular cross section. These cross sections can be divided into minute cross sections and these cross sections are responsible for holding the water column so weight gets uniform distributed. Functioning of mercury barometer: Downward pressure of mercury in the column = Outside atmospheric pressure Mercury column inside the capillary comes to rest. Net forces are balanced Applying force balance Patm×A=m×g Patm=Atmospheric pressure A=Area of cross section mg gives the weight m=ρ×V and V =A×h ρ=density V=volume Patm×A=(ρ×g×h)×A Patm=ρgh Patm=13.6×9.8×h=101325 N/m2 (at sea level) So the height upto mercury rises = 760 mm=760×10−3 m Here the P∘=mg are in equilibrium

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