__Question 6.3__:

__Solution__:**(a)**

*x*>

*a*; 0

*E*= P.E. + K. E.

∴ K.E. =

*E*– P.E.

Kinetic energy of a body is a positive quantity. It cannot be negative. Therefore, the particle will not exist in a region where K.E. becomes negative.

In the given case, the potential energy (

*V*

_{0}) of the particle becomes greater than total energy (

*E*) for

*x > a*. Hence, kinetic energy becomes negative in this region. Therefore, the particle will not exist is this region. The minimum total energy of the particle is zero.

**(b)**All regions

**In the given case, the potential energy (**

*V*

_{0}) is greater than total energy (

*E*) in all regions. Hence, the particle will not exist in this region.

**(c)**

*x*>

*a*and

*x*<

*b*; –

*V*

_{1}

In the given case, the condition regarding the positivity of K.E. is satisfied only in the region between

*x*>

*a*and

*x*<

*b.*

The minimum potential energy in this case is –

*V*

_{1}. Therfore, K.E. =

*E*– (–

*V*

_{1}) =

*E*+

_{ }

*V*

_{1}. Therefore, for the positivity of the kinetic energy, the totaol energy of the particle must be greater than –

*V*

_{1}. So, the minimum total energy the particle must have is –

*V*

_{1}.

**(d)**-b/2 < x < a/2 ; a/2 < x < b/2 ; -V

_{1}

_{}In the given case, the potential energy (

*V*

_{0}) of the particle becomes greater than the total energy (

*E*) for -b/2 < x < b/2 and -a/2 < x < a/2. Therefore, the particle will not exist in these regions.

The minimum potential energy in this case is –

*V*

_{1}. Therfore, K.E. =

*E*– (–

*V*

_{1}) =

*E*+

_{ }

*V*

_{1}. Therefore, for the positivity of the kinetic energy, the totaol energy of the particle must be greater than –

*V*

_{1}. So, the minimum total energy the particle must have is –

*V*

_{1}.

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