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The speed v of a freely falling body is assumed to vary as v proportional to g^p * h^q, where g is the acceleration due to gravity and h is the height fallen. Using dimensional analysis, find the value of p + q.

1. 0
2. 1
3. 1/2
4. -1

Correct answer: 1

Solution

Dimensional matching gives p = 1/2 and q = 1/2, so p + q = 1. This is consistent with v = sqrt(2gh).

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