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

Options

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

Answer

D

Explanation

` m prop v^(a) rho^(p) g^(c ) ML^(0) T^(0) prop (LT^(-1))^(a) (ML^(-3))^(b) (LT^(-2))^( c )`
Comparing the powers of `M , L , and T` and solving , we get ` b = 1 , c = -3 , a = 6 rArr m prop v^(6)`