Question

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 (s) 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 at x = a
B	U2(x)=U0/2(x/a)2	Q	the force acting on the particle is zero at x = 0.
C	U3(x)=U0/2(x/a)2 exp [-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]	S	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.

Answer 1

(A) →P,Q,R, T (B)→Q,S ; (C) →P, Q R, S ; (D)→P, R, T