A particle of unit mass is moving along the -axis under the influence of a force and…

PHYSICS · Subjective · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A particle of unit mass is moving along the xx -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 ( aa and U0U_0 constants). Match the potential energies in column I to the corresponding statement(s) in column II. #### Column I (A) U1(x)=U02[1−(xa)2]2U_1(x) = \frac{U_0}{2} \left[ 1 - \left( \frac{x}{a} \right)^2 \right]^2 (B) U2(x)=U02(xa)2U_2(x) = \frac{U_0}{2} \left( \frac{x}{a} \right)^2 (C) U3(x)=U02(xa)2exp⁡[−(xa)2]U_3(x) = \frac{U_0}{2} \left( \frac{x}{a} \right)^2 \exp \left[ -\left( \frac{x}{a} \right)^2 \right] (D) U4(x)=U02[xa−13(xa)3]U_4(x) = \frac{U_0}{2} \left[ \frac{x}{a} - \frac{1}{3} \left( \frac{x}{a} \right)^3 \right] #### Column II (p) The force acting on the particle is zero at x=ax = a (q) The force acting on the particle is zero at x=0x = 0 (r) The force acting on the particle is zero at x=−ax = -a (s) The particle experiences an attractive force towards x=0x = 0 in the region ∣x∣<a|x| < a (t) The particle with total energy U04\frac{U_0}{4} can oscillate about the point x=−ax = -a

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