Given in figure. Are examples of some potential energy functions in one dimension (i) to (iv). The total energy E of the particle is indicated by the cross mark on energy axis. In each case, specify the refions, if any, in which the particle cannot be found for the given energy. Also, indicatethe minimum total energy the particle must have in each case. Think of simple physical contests for which these potential energy shapes are relevant.

Given in figure. Are examples of some potential energy functions in on

1.	Given in figure. Are examples of some potential energy functions in one dimension (i) to (iv). The total energy E of the particle is indicated by the cross mark on energy axis. In each case, specify the refions, if any, in which the particle cannot be found for the given energy. Also, indicatethe minimum total energy the particle must have in each case. Think of simple physical contests for which these potential energy shapes are relevant.
Answer» Solution :We know that total ENERGY `E=K.E.+P.E.` or `K.E.=E-P.E.` and `K.E.` can never be negative. The object cannot exist in the region, where its K.E. would becomenegative. (i) For`X gt a`, P.E. `(V_(0) gt E` `:.` K.E. becomes negative. Hence, the objectconnot exist in the region `xgta`. (II)For `x lt a` and `x gt bP.E. (V_(0)) gt E.` `:.` K.E. becomes negative. Hencethe objectcannot 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`.