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Question

The potential energy of a particle as a function of its position is given by U=x36x2 (in SI units). The nature of equilibrium at x=4 is

A
Stable
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B
Unstable
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C
Neutral
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D
Insufficient Data
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Solution

The correct option is A Stable
U=x36x2
We know that,
F=Ux=(3x212x)
F=12x3x2
The nature of equilibrium is stable if F=0 & 2Ux2 is positive
So, when F=0
3x(4x)=0
x=0 & x=4
Now,
2Ux2=xUx=x(3x212x)
= 6x12|x=4
= 2412=12>0
Therefore condition of stable equilibrium.

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