Given in Fig. are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any in which the particle cannot be found for the given energy. Also , indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant

Explanation

We know that total energy E = P.E + K.E (or) K.E = E - P.E and K.E can never by negative . The object cannot exist in the region where its E.E would become negative
(i) For `x lt a`, P.E `(v_(0)) gt E`
`:. K.E` becomes negative. Hence the object cannot exist in the region `x gt a`
(ii) For `x lt a and x gt b, P.E (v_(0)) gt E`
`:.` K.E becomes negative. Hence the object cannot be present in the region `x gt a and x gt b`
(iii) Object cannot exist in any region because `P.E (v_(0)) gt E ` in every region
(iv) On the same basis, the object cannot exist in the region `- b //2 lt x lt - a//2 and a//2 lt x lt b//2 `