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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