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Q.

A gas bubble from an explosion under water oscillates with a period T proportional to Pa dbEc , where P is the static pressure, d is the density and E is the total energy of the explosion. The -values of a, b and c are :

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a

a = 0, b = I, c = 2

b

a = I, b = 2, c = 3

c

a = 5/6, b = -1/2, c = 1/3

d

a = -5/6,b = 1 /2,c = ⅓

answer is D.

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Detailed Solution

T ∝ Pa db Ec⇒[T]= [(ML-1T-2 )a(ML-3)b(ML2T-2)c]⇒ [M0L0T]= [Ma+b+cL-a-3b+2cT-2a-2c]⇒ a + b + c = 0, - a - 3b + 2c = 0 and - 2a - 2c = 1

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A gas bubble from an explosion under water oscillates with a period T proportional to Pa dbEc , where P is the static pressure, d is the density and E is the total energy of the explosion. The -values of a, b and c are :