A gas bubble, from an explosion under water, oscillates with a period T proportional to p a d b E c , where p is the static pressure, d is the density of water and E is the total energy of the explosi

Question

A gas bubble, from an explosion under water, oscillates with a period T proportional to p a d b E c , where p is the static pressure, d is the density of water and E is the total energy of the explosion. Find the values of a , b and c .

TestHub · Accepted Answer

[ T ] = [ p a d b E c ] = ( [ M L − 1 T − 2 ] ) a ( [ M L − 3 ] ) b ( [ M L 2 T − 2 ] ) c . Equating powers: a + b + c = 0 , − a − 3 b + 2 c = 0 , − 2 a − 2 c = 1 . Solving: a = − 6 5 ​ , b = 2 1 ​ , c = 3 1 ​ .

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