Water is filled up to a height in a beaker of radius as shown in the figure. The density of water is , the surface tension of water is and the atmospheric pressure is . Consider a vertical section ABCD of the water column through a diameter of the beak

Question

Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $ρ$ , the surface tension of water is $T$ and the atmospheric pressure is $P_{0}$ . Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude [2007]

Smart Achievers · Accepted Answer

(2)

In the first part the force is created due to pressure and in the second part the force is due to surface tension T.

$The force is [(P_{0} + \frac{h ρ g}{2}) \times (2 R \times h)] - 2 R T$

$∴$ $Force = 2 P_{0} R h + R ρ g h^{2} - 2 R T$

Solution

1 $| 2 P_{0} R h + π R^{2} ρ g h - 2 R T |$

2 $| 2 P_{0} R h + R ρ g h^{2} - 2 R T |$

3 $| P_{0} π R^{2} + R ρ g h^{2} - 2 R T |$

4 $| P_{0} π R^{2} + R ρ g h^{2} + 2 R T |$

Ans.
(2)

In the first part the force is created due to pressure and in the second part the force is due to surface tension T.

$The force is [(P_{0} + \frac{h ρ g}{2}) \times (2 R \times h)] - 2 R T$

$∴$ $Force = 2 P_{0} R h + R ρ g h^{2} - 2 R T$

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Solution

1 |2P0Rh+πR2ρgh-2RT|

2 |2P0Rh+Rρgh2-2RT|

3 |P0πR2+Rρgh2-2RT|

4 |P0πR2+Rρgh2+2RT|