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. `upsilon^4`
B. `upsilon^6`
C. `upsilon^5`
D. `upsilon`

Answer

(b)

Explanation

Let `m = k upsilon^a rho^b g^c `, where k is dimnsionless constant.
`[M^1 L^0 T^0] = (LT^(-1))^a (ML^(-3))^b (LT^(-2))^c`
`M^b L^(a -3b+c) T^(-a-2c)`
Applying the principle of homogeneity of dimensions, we get
`b= 1 , - a-2c = 0 or c = (-a)/(2)`
` a- 3b + c = 0`
`a - 3- a//2 =0` or `a =6`
Hence, `m prop upsilon^6`