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) | (P) | the force acting on the particle is zero at x = a. | |
(b) | (Q) | the force acting on the particle is zero at x = 0. | |
(c) | (R) | the force acting on the particle is zero at x=–a. | |
(d) | (S) | The particle experiences an attractive force towards x = 0 in the region a | |
(T) | The particle with total energy can oscillate about the point x = –a. |
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
→ P, Q, R, T, → Q, S, → P, Q, R, S, → P, R, T
Sol. F x = 
= – 
[x–a] [x] [x + a]
→ (P) (Q) (R) (T)
F x = 
= 
F x = 
= U 0 
[x][x – a] [x + a]
F x = 
=
= 
P, R, T
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