Question

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

Answer 1

Correct Answer - D
`m" "alpha" "v^(a)rho^(b)g^(c)`. Writing the dimensions on both sides
`["M"]=["LT"^(-1)]^(a)["ML"^(-3)]^(b)["LT"^(-2)]^(c)`
`["M"]=["M"^(b)"L"^(a-3b+c)"T"^(-a-2c)]`
`therefore" "b=1`
`a-3b+c=0Rightarrow-a-2c=0`
Solving these, we get
`" "a=6`
Hence, `" "m" "alpha" "v^(6)`