A particle is moving in a circle of radius ‘r’ under the action of a forceF =  αr2,  which is directed towards centre of the circle.  Total mechanical energy of the particle is (take P.E.  =  0    at  r = 0)

Centripetal force   F =  αr2  ∴    mv2r   =    αr2   ⇒   mv2   =    α⋅r3   ∴   K.E.   =    12 mv2    =   12  αr3     ∴   P.E.   =   U =∫ F.dr  PE =  ∫ αr2⋅ dr  PE =    αr33  ∴      Total energy =P.E.  +K.E substitute above obtained values,  TE  =   αr33 +  12  αr3 TE= 56  αr3