The kinetic energy of a particle moving along a circle of radius R depends on the distance covered s as `T=as^2`, where a is ticle as a function of s.

Explanation

We have
`T=1/2mv^2=as^2` or, `v^2=(2as^2)/(m)` (1)
Differentiating Eq. (1) with respect to time
`2vw_t=(4as)/(m)v` or, `w_t=(2as)/(m)` (2)
Hence net acceleration of the particle
`w=sqrt(w_t^2+w_n^2)=sqrt(((2as)/(m))^2+((2as)/(mR))^2)=(2as)/(m)sqrt(1+(s//R)^2)`
Hence the sought force, `F=mw=2assqrt(1+(s//R)^2)`