Question

When an object falls through air, there is a drag force that depends on the product of the cross sectional area of the object and the square of its velocity, that is, Fair = CAv2, where C is a constant. Determine the dimensions of C. (Use the following as necessary: M for mass, T for time, and L for length.)

Answer 1

Answer:

$\textrm{Dimension of C }=\ [ML^{-3}T^{0}]$

Step-by-step explanation:

As given in question drag force depends upon the product of the cross sectional area of the object and the square of its velocity

and drag force can be given by

$F=CAv^2$          (1)

It is given that

Dimension of mass = [M]

Dimension of length = [L]

Dimension of time = [T]

So, by using above dimension we can write

the dimension of force,

$F=[MLT^{-2}]$

dimension of cross-section area,

$A=[L^2]$

and dimension of velocity

$v=[LT^{-1}]$

now, by putting these values in equation (1), we will get

$F=CAv^2$

$=>[MLT^{-2}]=C[L^2][LT^{-1}]^2$

$=>C=[ML^{-3}T^0]$

Hence, the dimension of constant C will be,

$C=[ML^{-3}T^0]$