Why is the work done by a centripetal force equal to zero?

Explanation

the centripetal force `vecF_c` and linear velocity `vecv` of a particle in circular motion are perpendicular to each at every instant, the force being radially inward and velocity tengantial. Therefore, `vecF_c.vecv=0` at every instant. Since `vecv=vec(ds)//dt,` the work done by the centripetal force, `W=vecF_c.vec(ds)=vecF_c.vecvdt=0.`