Question

Suppose we are told that the speed, v, of a rotating particle depends on the radius, r,

and the frequency f, in the form v = 2πr

a

/fb

. If this is to be a dimensionally homogeneous

equation, determine the values of a and b.

Answer 1

As per the given question,

Here the f is the frequency of the rotating particle and r is the radius and v is the velocity of the particle which is rotating in the circular path.

So, $v=\frac{2\pi ra}{fb}$

the dimensional formula of $v=[LT^{-1}]$

dimension formula of $r=[L]$

Dimensional formula of f is $[T^{-1}]$

Now, substituting the values,

$[LT^{-1}]=\frac{[L]a}{[T^{-1}]b}$

So, dimensional formula of a$=[T^{-1}]$

Dimension formula of b $=[T]$