Concept explainers
Consider two tubes of equal cross-sectional area. One is a 76-cm-tall tube of mercury and the other a 10.3-cm-tall tube of water. Which weighs more? Which exerts more pressure at the bottom of the tube?
The tube that weighs more and exert more pressure.
Answer to Problem 15RQ
Both the tubes weighs same and exerts equal amount of pressure at bottom.
Explanation of Solution
Given Info: The length of the tube of mercury is 76 cm and the length of the tube of water is 10.3 cm .
Write the expression for the pressure exerted by the mercury.
Here,
h is the height of the tube
is the density of the mercury
g is the acceleration due to gravity
Substitute, 76 cm for h , 13600 kg/m3 for , and 9.8 m/s2 for g in the above expression to get Pm .
Write the expression for the pressure exerted by the water.
Here,
h is the height of the tube
is the density of the mercury
g is the acceleration due to gravity
Substitute, 10.3 m for h ,1000 kg/m3 for , and 9.8 m/s2 for g in the above expression to get Pm .
Thus, both the tubes exert equal amount of pressure at bottom.
Write the formula for the force exerted by the mercury.
……(i)
Here,
Pm is the pressure exerted by the mercury
Am is the area of cross-section of tube.
Write the formula for the force exerted by the water.
……(ii)
Here,
Pw is the pressure exerted by the water
Pw is the area of cross-section of tube.
As the cross-sectional area of both the tubes are same, and the pressure exerted by both the liquids is also equal, then the force exerted by mercury and water will be same.
By using equation (i) and (ii),
The force exerted by the liquid at the bottom of the tube is the weight of the liquid. Thus, both the liquid weighs same.
Conclusion:
Therefore, both the tubes weighs same and exerts equal amount of pressure at bottom.
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