the work required to move the particle from equilibrium position to infinity is?the nature of the force is?if the potential energy function of the particle is given by U(r)=A/r(square)-B/r,where AandB ARE POSITIVE constants.?

find f= -du/dr

for equil.pos. put f=0   ,   so r=2A/B

to find nature of force displace particle by distance x from equil.pos.

as it is displaced force will be applied so equating to ma.

   -[-2A/(2A/B+x)³ + B/(2A/B+x)²  ]= ma

using binomial expansions and approximation simplyfy to get

ma= -(B⁴/8A³)x   thus it is an shm.

simply as:

take it as num (2A/B+x)^-3  and simplyfy as =  (2A/B-3x) and do the rest.

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