Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon the velocity `upsilon,` of water, its density `rho` and acceleration due to gravity g, then m is directly proportional to

Explanation

Let `M propto v^(a)p^(b)g^(c )`
`implies [M] propto [v]^(a)[p]^(b)[g]^(c )`
`implies [M]=[LT^(-1)]^(a)[ML^(-3)]^(b)[LT^(-2)]^(c )`
`implies [ML^(0)T^(0)]= [M^(b)L^(a-3b+c)T^(-a-2c)]`
Comparing the dimensions on both the sides we get the following :
`b=1`
`a-3b+c=0 implies a-3+c=0`
`implies a+c= 3`
Also,
`-a -2c=0`
Adding the above two equations we get `-c=3 implies c= -3`.
`implies -a-2xx -3=0 implies a=6`
Hence the value of n =6.