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JEE Advanced2007PhysicsMechanical Properties of FluidsActual

Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is , the surface tension of water is T and the atmospheric pressure is p₀ . Consider a vertical section A B C D 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.

Options

  1. A|2 p₀ R h+ R^2 g h-2 R T |
  2. B|2 p₀ R h+R g h^2-2 R T |
  3. C|p₀ R^2+R g h^2-2 R T |
  4. D|p₀ R^2+R g h^2+2 R T |

Correct answer

B. |2 p₀ R h+R g h^2-2 R T |

Step-by-step solution

Force from right hand side liquid on left hand side liquid. (i) Due to surface tension force =2 R T (towards right) (ii) Due to liquid pressure force aligned & = _ x=0 ^ x=h (p₀+ g h )(2 R x) d x & = (2 p₀ R h+R g h^2 ) (towards left) aligned Net force is |2 p₀ R h+R g h^2-2 R T | Correct option is (b).

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