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.

Answer

`F= K (mv^(2))/(r )`

Explanation

`F prop m^(a) v^(b)r^(c ) rArr F = km^(a) v^(b) r^(c ) `
`rArr [M^(1)L^(1) T^(-2)] = [M]^(a) [ L^(1)T^(-1)]^(b) [L]^(c ) = [M]^(a) [L]^(b+c) [T]^(-b) `
by comparision a = 1, b = 2, c= -1
So `F= k(mv^(2)) /(r )`