The largest stone of mass m that can be moved by a flowing river is assumed to depend on the velocity of flow v, the density of water d, and the acceleration due to gravity g. Using dimensional analysis, if m varies as v^K, find K.

K = 6
K = 3
K = 4
K = 2

Correct answer: K = 6

Solution

Setting up dimensional equations: [M¹] gives b=1; [T⁰] gives a+2c=0; [L⁰] gives a-3+c=0. Solving: c=-3, a=6, so m ~ v⁶ and K=6.

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