Question

Match the following: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
(A)$U_{1} (x) =\frac{ U_0}{2} \bigg [1-(\frac{x}{a})^{2} \bigg ]^{2}$ (B)$U_{2} (x) =\frac{U_0}{2} (\frac{x}{a})^{2}$
(C)$U_{3} (x) =\frac{U_0}{2} (\frac{x}{a})^{2}exp \bigg [- (\frac{x}{a})^{2} \bigg]$
(D)$U_{4} (x) =\frac{U_0}{2} \bigg [\frac{x}{a}-\frac{1}{3}( \frac{x}{a})^{3} \bigg ]$

Column II
(p) The force acting on the particle is zero at x = a.
(q) The force acting on the particle is zero at x=0.
(r) The force acting on the particle is zero at x =-a.
(s) The particle experiences an attractive force towards x = 0 in the region $|x| \ \textless \ a$ .
(t) The particle with total energy $\frac{U_0}{4}$ can oscillate about the point x = −a.

Answer 1

Answer:

75665

Explanation:

Answer 2

Answer:

PQRT

QS

PQRS

PRT

Explanation:

FORCE = -DU/DX

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