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.

Let F=k(m)x(v)y(r)z… (i) Here, k is a dimensionless constant of proportionality. Writing the dimensions of RHS and LHS in Eq. (i), we haveMLT-2=[M]xLT-1y[ L]z=Mx Ly+2 T-yEquating the powers of M, L and T of both sides, we have, x=1,y=2  and  y+z=1  or  z=1-y=-1Putting the values in Eq. (i), we getF=kmv2r-1=kmv2rorF=mv2r (where, k=1 )