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QAIPM-2012-Ph-1743: NEET 2012 Physics - Class 11 AIPM-2012-Ph-1743 Solution: The potential energy of a particle in a force field is \(U=…
The potential energy of a particle in a force field is where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is
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Step-by-Step Verified Solution
Here, U = A r 2 _ B r
For equilibrium, d U d r = 0
_ _ 2 A r 3 + B r 2 = 0
_ 2 A r 3 = B r 2 _ r = 2 A B
For stable equilibrium, d 2 U d r 2 > 0
d 2 U d r 2 = 6 A r 4 _ 2 B r 3
d 2 U d r 2 | r = ( 2 A / B ) = 6 A B 4 16 A 4 _ 2 B 4 8 A 3 = B 4 8 A 3 > 0
So for stable equilibrium, the distance of the particle
is 2 A B .