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Two rain drops reach the earth with different terminal velocities having ratio 9 : 4 . Then the ratio of their volumes is

Options

  1. A3 : 2
  2. B4   :   9
  3. C9   :   4
  4. D27   :   8

Correct answer

D. 27   :   8

Step-by-step solution

We know that terminal velocity is given by V T = 2 9 n r 2 ρ s - ρ l ∴ V T ∝ r ⁡ 2 ∴ 9 4 = r ⁡ 1 r ⁡ 2 2 ∴ r ⁡ 1 r ⁡ 2 = 3 2 ∴ V 1 V ⁡ 2 = r ⁡ 1 r ⁡ 2 3 = 3 2 3 V 1 V 2 = 27 : 8

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