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A gas bubble from an explosion under water, oscillates with a period proportional to P^arho^b E^cwhere p is the state pressure, rho is the density of water and is the total energy of the explosion. Find the values of a, b, and c.

Answer» <html><body><p></p>Solution :Let, `T <a href="https://interviewquestions.tuteehub.com/tag/alpha-858274" style="font-weight:bold;" target="_blank" title="Click to know more about ALPHA">ALPHA</a> P^(a) rho^(b) E^( <a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>)` <br/> Dimensional formula of <br/> `p to ML^(-1) T^(-<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>) , rho to ML^(-<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>) , E to ML^(2) T^(-2)` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> T^(1) alpha (ML^(-1) T^(-2) )^(a) (ML^(-3) )^(b) (ML^(2) T^(-2) )^( c)` <br/> Comparing powers of M, L and T on both sides <br/> `a+b+c =0 ""...(1)` <br/> `-a -3b+ 2c =0""....(2)` <br/> `-2a -2 c =1 ""...(3)` <br/> From (3) and (1), <br/> `a+c = - (1)/(2) and b= (1)/(2) = - (1)/(2) , (-a+ 2c = 3 xx (1)/(2) )/( 3c=1)`<br/> `rArr c = (1)/(3) and a = - (1)/(3) - (1)/(2) = -(5)/(6)` <br/> `therefore` The values of a, b, e are respectively, `- (5)/(6) , (1)/(2) , (1)/(3)`.</body></html>


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