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

Options

A. `F prop (1)/(v)`
B. `F prop v`
C. `F prop v^(2)`
D. `F prop (1)/(v^(2))`

Answer

C

Explanation

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)`