Question

A body moving through air at a high speed, V experiences a retarding force F given by F=KApV^x, where A is the surface area of the body, p is the density of the air and K is a numerical constant. Deduce the value of x

Answer 1

With the use of dimensional analysis we get

F=KApV^x → [N]=[m^2 ]∙[kg/m^3 ]∙[m^x/s^x ],

K is a dimensionless coefficient. So

(kg∙m)/s^2 =[m^2 ]∙[kg/m^3 ]∙[m^x/s^x ]

[(kg∙m)/s^2 ]=[kg/m]∙[m^x/s^x ]=[(kg∙m^(x-1))/s^x ] → x=2.

Answer. x=2.