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## Homework Statement

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

## Homework Equations

The problem is solved in the book. But I dont understand the solution properly.This problem was solved in the example as below:

[tex]a = k(r^n)(v^m)[/tex][tex]L/T^2 = (L^n)(L/T)^m = L^{n+m}/T^m[/tex][tex]n+m = 1 [/tex][tex] m = 2[/tex][tex]n = -1[/tex][tex]a = kr^{-1}v^2[/tex]

## The Attempt at a Solution

From the question

**we don't know if k has any dimension or not**. So how did they (in the second line) write [tex]L/T^2=(L^n)(L/T)^m ?[/tex]

**Where did the k go??**