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A gas bubble formed by an underwater explosion oscillates with a time 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 energy of the explosion. Using dimensional analysis, find the values of a, b, c.

1. 1, 1, 1
2. 1/3, 1/2, -5/6
3. -5/6, 1/2, 1/3
4. 1/2, -5/6, 1/3

Correct answer: -5/6, 1/2, 1/3

Solution

Matching dimensions on both sides of T = k * P^a * d^b * E^c and solving the three simultaneous equations for M, L, T gives a = -5/6, b = 1/2, c = 1/3.

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