Work Power and Energy 5 Question 14

17. 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 in Column II

(2015 Adv.)

Column I Column II
A. U1(x)=U021x2a P. The force acting on the particle is zero at x=a
B. U2(x)=U02x2a Q. The force acting on the particle is zero at x=0
C. U3(x)=U02x2a2expx2a R. The force acting on the particle is zero at x=a
D. U4(x)=U02xa13x3a S. The particle experiences an attractive force towards
x=0 in the region |x|<a
T. The particle with total energy U04 can oscillate about the
point x=a.
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Answer:

Correct Answer: 17. A-P, Q, R, T B-Q, S C-P, Q, R, S DP,R,T

Solution:

  1. (A) Fx=dUdx=2U0a3[xa][x][x+a]

F=0 at x=0,x=a,x=aU=0 at x=a

 and x=a

(B) Fx=dUdxU0xa

(C) Fx=dUdx=U0ex2/x2a3[x][xa][x+a]

(D) Fx=dUdx=U02a3[(xa)(x+a)]

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