Question the dimension

Electricity and Magnetism Level pending

Suppose we are told that the acceleration a a of a particle moving with uniform speed v v in a circle of radius r r is proportional to some power of r r , say r n r^n , and some power of v v , say v m v^m . What are the values of n n and m m ?

n=-1, m=2 n=2, m=-1 n=2, m=2 n=-1, m=1

Saurabh Kumar Agrawal by saurabh kumar agrawal , 27, India

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1 solution

Chew-Seong Cheong
Aug 18, 2014

The centripetal acceleration a a is given by

a = v 2 r ⇒ n = − 1 , m = 2 a=\cfrac{v^2}{r} \quad \Rightarrow \quad n = -1, m = 2 .

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