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Question

The potential energy of a particle is given by relation U=x36x2 (In SI units). The nature of equilibrium at x=0 is

A
Stable
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B
Unstable
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C
Neutral
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D
Undefined
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Solution

The correct option is B Unstable
It is given that, U=x36x2

We also know that F=dUdx=3x2+12x
dUdx=3x212x

For the condition of equilibrium, force F=0F=3x2+12x=0

F=03x(4x)=0
x=0 ,x=4

d2Udx2=ddx(3x212x)=6x12

At (x=0)
d2Udx2=12<0
F=0 & d2Udx2<0 is the condition for unstable equilibrium

Unstable Equillibrium

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