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The speed of surface water waves is assumed to depend on the wavelength lambda, the density of water rho, and the acceleration due to gravity g as v = lambda^a * rho^b * g^c. Using dimensional analysis, find the value of a + b + c.

1. 0
2. 1
3. 2
4. 3

Correct answer: 1

Solution

By matching dimensions, b = 0, c = 1/2, and a = 1/2, giving a + b + c = 1.

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