A stone is lying in a fluid stream. The force acting on it depends on the density of the fluid, the velocity of flow and the maximum area of cross-section perpendicular to the direction of flow. The force F and the velocity v of flow are related as

A stone is lying in a fluid stream. The force acting on it depends on

1.	A stone is lying in a fluid stream. The force acting on it depends on the density of the fluid, the velocity of flow and the maximum area of cross-section perpendicular to the direction of flow. The force F and the velocity v of flow are related as
Answer» `F prop (1)/(V)` `F prop v` `F prop v^(2)` `F prop (1)/(v^(2))` Solution :LET `F= kd^(a)v^(b)A^(c)` Where K is a dimensional constant `:. [MLT^(-2)]= [ML^(-3)]^(a)[LT^(-2)]^(b)[L^(2)]^(c)= [M^(a)L^(-3a+b+2c)T^(-b)]` Applying the principle of HOMOGENEITY of dimensions, we get a=1 and -b= -2 or b=2 `:. F prop v^(2)`