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 (a and U0 are constants). Match the potential energies in column I to the corresponding statements (*) in column II.
| | Column-I | | Column-II | | A | U1(x)=U0/2 [1-(x/a)2]2 | p | the force acting on the particle is zero atx = a | | B | U2(x)=U0/2(x/a)2 | Q | the force acting on the particle is zero atx = 0. | | C | U3(x)=U0/2(x/a)2exp [-x/a)2] | R | the force acting on the particle is zero at x= – a | | D | U4(x)=U0/2[x/a-1/3(x/a)3] | * | The particle experiences an attractive force towards x = 0 in the region |x|<a | | | | | The particle with total energy U0/4 oscillate about the point x = – a. |
(A) →P,Q,R, T (B)→Q, ; (C) →P, Q R, ; (D)→P, R, T
