A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I ( α and U0 are constants). Match the potential energies in column I to the corresponding statement(s) in column II.

A) U=U021+x4a4−2x2a2F=−dUdx=−U020+4x3a4−4xa2=2U0a2x−x3a2F=0 at both x=+a,0,-a; ⇒P,Q,R are suitable.At  x=a2,F=2U0a2x1−x2a2=2U0a2×a21−14F=3U04a⇒F is +ve i.e., ‘F’ is not directed towards ‘O’∴ ‘S’ is not suitable.At  x=−a, particle is in stable equilibrium and U=0TE=U04⇒KE=U04 At x=0,U=U02⇒ particle cannot reach ‘O’.∴  Particle executes oscillatory motion about x=-a.B) U=U02xa2⇒F=−dUdx=−U0xa2At x=a, F=−U0a⇒'P' does not suitAt x=0, F=0  ⇒'Q' is suitableAt x=-a, F=U0A⇒'R' is not suitable.At  x