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Due to an explosion underneath water, a bubble started oscillating. If this oscillation has time period T , which is proportional to p^ S^ E^ , where p is static pressure, S is density of water and E is total energy of explosion. Determine , and .

Options

  1. A=- 3 2 , = 1 3 , =- 5 6
  2. B=- 5 6 , = 1 2 , = 1 3
  3. C= 1 2 , =- 5 6 , = 7 4
  4. D= 1 3 , = 3 2 , = 4 3

Correct answer

B. =- 5 6 , = 1 2 , = 1 3

Step-by-step solution

Given, time-period of oscillation T is T p^ S^ E^ or T=k p^ S^ E^ Now, subtituting dimensions of T, p, S and E , we have [ M ^0 ~L ^0 ~T ^ l ]=k [ ML ⁻¹ ~T ⁻² ]^ [ ML ⁻³ ]^ [ ML ^2 ~T ⁻² ]^ Equating powers of similar terms, we have Solving, we get = -5 6 , = 1 2 , = 1 3

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