If L, m denote the angular momentum and mass of the particle a:rd p is linear momentum, which of the following can represent the kinetic energy of the particle moving in a circle of radius .R ?

In terms of linear momentum, the K.E. is given by  K.E. =p22mNow we consider the K.E in terms of angular momentum L L=mvR  or  V=L/(mR) K.E. =12mv2 Substituting the value of v from eq. (1) in eq. (2), we get   K.E. =12m(L/mR)2=L22mR2