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)).

It is given that the mass m of the largest stone that can be moved by

1.	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)).
Answer» Solution :`m=kv^(X)rho^(y)g^(Z)` Taking dimensions on both sides …I `L^(0)T^(0)M=[LT^(-1)]^(x)[ML^(-3)]^(y)[LT^(-2)]^(z)` `L^(0)T^(0)M=L^(x-3y+z)M^(y)T^(-x-2z)` Equating the dimensions of M,T and L on both sides `y=1` ……ii `-x-2z=0` or `x+2z=0` `x=3y=z=0` `x+z=3y=3`.......iii EQUATION ii minus equqtion (iii) `x+2z-x-z=0-3,z=3,x=-2z=6` Substituting the value of x, y and z in equation (i) `m=kv^(6)rho^(1)g^(-3)=K(v^(6)beta)/(g^(3))`