The centripetal force F acting on a particle moving uniformly in a circle may depend upon mass (m), velocity (v) and radius ( r) of the circle . Derive the formula for F using the method of dimensions.

Explanation

Accroding to the provided information,
let `F prop m^(a) v^(b) r^(c). implies km^(a) v^(b) r^(c)`
`implies [M^(1) L^(1) T^(-2)] = [M^(a) (LT^(-1))^(b) L^(c)]`
`implies [M^(1) L^(1) T^(-2)] = [M^(a)N L^(b+c) T^(-b)]`
using principle of homongenity we have
`a = 1, b + c = 1, b = 2`
using these, values we get `F = km^(1) v^(2) r^(-1)`
`implies F = k(mv^(2))/(r)`