Suppose we are told that the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r, say rn, and some power of v, say vm. determine the values of n and m and write the simplest form of an equation for the acceleration.

Acceleration,

Explanation:

It is given that, the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r and some power of v. Mathematically, it can be written as :

or

...........(1)

Dimensional formula of a =

Dimensional formula of r =

Dimensional formula of v =

Using dimensional analysis in equation (1) as :

Equation both sides of equation as :

n + m = 1,  m = 2

This gives, n = -1

Use the value of m and n in equation (1) in order to get the formula :

Hence, this is the required solution.