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The ratio of surface tensions of mercury and water is given to be 7.5 , while the ratio of their densities is 13.6 . Their contact angles, with glass, are close to 135 ° and 0 ° , respectively. If it is observed that mercury gets depressed by an amount h in a capillary tube of radius r 1 , while water rises by the same amount h in a capillary tube of radius r 2 , then the ratio r 1 r 2 is close to

Options

  1. A3 / 5
  2. B2 / 3
  3. C4 / 5
  4. D2 / 5

Correct answer

D. 2 / 5

Step-by-step solution

| h Hg | = | h water | 2 S 1 c o s θ 1 ρ 1 r 1 g = 2 S 2 c o s θ 2 ρ 2 r 2 g Therefore, the ratio of the radii of the respective tubes is, r 1 r 2 = ρ 2 ρ 1 × S 1 cos θ 1 S 2 cos θ 2 r 1 r 2 = 1 13.6 × 7.5 × 1 2 r 1 r 2 ≈ 2 5

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