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 statement(s) in column II.
Column I | Column II |
(A) U1(x)=U02[1−(xa)2]2 | (P) The force acting on the particle is zero at x = a. |
(B) U2(x)=U02(xa)2 | (Q) The force acting on the particle is zero at x = 0. |
(C) U3(x)=U02(xa)2 exp[−(xa)2] | (R) The force acting on the particle is zero at x = – a. |
(D) U4(x)=U02[xa−13(xa)3] | (S) The particle experiences an attractive force towards x = 0 in the region |x|<a. |
(T) The particle with total energy U04can oscillate about the point x = – a. |