The acceleration (a) of a particle moving with uniform speed (v) in a circle of radius (r) is found to be propotional to r^n and v^m, where n and m are constants. Determine the values of n and m and write the simplest form of an equation of acceleration

n=-1 and m=2

Explanation:

A particle is moving uniformly with acceleration "a"

Uniform speed is v

And radius of circle is r

The acceleration is proportional to

r^n and v^m

i.e

a∝ rⁿ

a ∝v^m

Combing the two

Then, a∝rⁿv^m

Let k be constant of proportionality

Then, a=krⁿv^m. Equation 1

So, we know that the centripetal acceleration keeping an object in circular path is given as

a=v²/r

Rearranging

a=v²r^-1. Equation 2

So comparing this to the proportional

Equating equation 1 and 2

krⁿv^m = v²r^-1

This shows that,

k=1

rⁿ = r^-1

Then, n =-1

Also, v^m =v²

Then, m=2

Therefore,

n=-1 and m=2

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