It is given that the mass m of the largest stone that can be moved by the folowing river depends upon the velocity v, density `rho` and acceleration due gravity g. Using dimensions show that `m=(kv^(6)rho)/(g^(3))`.

Explanation

To solve the problem, we need to show that the mass \( m \) of the largest stone that can be moved by the river can be expressed in the form:

\[ m = \frac{k v^6 \rho}{g^3} \]

where \( k \) is a dimensionless constant, \( v \) is the velocity, \( \rho \) is the density, and \( g \) is the acceleration due to gravity.

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