$A$ 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 $U_0$ are constants). Match the potential energies in column $I$ to the corresponding statement$(s)$ in column $II$.

Column $I$	Column $II$
$(A) U_1(x) = \frac{U_0}{2} \left[1 - \left(\frac{x}{a}\right)^2\right]^2$	$(P)$ The force acting on the particle is zero at $x = a$.
$(B) U_2(x) = \frac{U_0}{2} \left(\frac{x}{a}\right)^2$	$(Q)$ The force acting on the particle is zero at $x = 0$.
$(C) U_3(x) = \frac{U_0}{2} \left(\frac{x}{a}\right)^2 \exp \left[-\left(\frac{x}{a}\right)^2\right]$	$(R)$ The force acting on the particle is zero at $x = -a$.
$(D) U_4(x) = \frac{U_0}{2} \left[\frac{x}{a} - \frac{1}{3}\left(\frac{x}{a}\right)^3\right]$	$(S)$ The particle experiences an attractive force towards $x = 0$ in the region $|x| < a$.
	$(T)$ The particle with total energy $\frac{U_0}{4}$ can oscillate about the point $x = -a$.

• A
  $(A) \rightarrow (P, Q, R, S); (B) \rightarrow (Q, T); (C) \rightarrow (P, Q, R, T); (D) \rightarrow (P, R, S)$
• B
  $(A) \rightarrow (P, Q, R, T); (B) \rightarrow (Q, S); (C) \rightarrow (P, Q, R, S); (D) \rightarrow (P, R, T)$
• C
  $(A) \rightarrow (P, R, S, T); (B) \rightarrow (Q, R); (C) \rightarrow (P, R, S, T); (D) \rightarrow (P, Q, T)$
• D
  $(A) \rightarrow (Q, R, S, T); (B) \rightarrow (S, T); (C) \rightarrow (Q, R, S, T); (D) \rightarrow (Q, R, T)$