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

Options

A. `v^(3)`
B. `v^(4)`
C. `v^(5)`
D. `v^(6)`

Answer

D

Explanation

`mpropv^(a)p^(b)g^(c)`. Writing the dimensions on both sides
`[M]=[LT^(-1)]^(a)[ML^(-3)][LT^(-2)]^(c)`
`[M]=[M^(b)L^(a)-^(3b+c)T^(-a-2c)]`
`:. b=1`
`a-3b+c=0implies-a-2c=0`Solving these, we get
`a=6 `
Hence, `mpropv^(6)`