Centripetal force (F) on a body of mass (m) moving with uniform speed (v) in a circle of radius (r ) depends upon m, v and r. The formula for the centripetal force using theory of dimensons.

Explanation

Let `F=km^(a)v^(b)r^(c )=m^(a)v^(b)r^(c ) [=1]`
Then `M^(1)L^(1)T^(-2)= [M]^(a)[LT^(-1)]^(b)[L]^(c )`
`=[M^(a)L^(b+c)T^(-b)]`
Comparing the exponents of M, L and T on both sides, we get
`a=1, b+c=1`
`b=2`
`implies c=1-b=1-2= -1`
`F= (mv^2)/(r )`
This is the required expression.