The kinetic energy of a particle moving along a circle of radius `R` depends on the distance covered `s` as `K=lambdas^(2)`, where `lambda` is a constant. Find the force acting on the particle as a function of `s`.

Explanation

`K.E.,K=(1)/(2)mv^(2)=lambdas^(2)impliesv=sqrt((2lambda)/(m))s`
`(dv)/(ds)=sqrt((2lambda)/(m))`
`a_(1)=v(dv)/(ds)=(2lambdas)/(m)`
`a_(c)=(v^(2))/(R )=(2lambdas^(2))/(mR)`
Acceleration `a=sqrt(a_(c)^(2)+a_(t)^(2))=(2lambdas)/(m)sqrt(1+((s)/(R ))^(2))`
force `F=ma=2lambdas sqrt(1+((s)/(R ))^(2))`