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Question

Potential energy of a particle moving along x axis is given by U=(x334x+6).
Here, U is in joules and x in metres. Find the position of stable and unstable equilibriums, respectively.

A
x=2 m and x=2 m
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B
x=2 m and x=2 m
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C
x=0 and x=0
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D
x=1 m and x=1 m
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Solution

The correct option is A x=2 m and x=2 m
U=x334x+6
F=dUdx=x2+4
F=0 at x=±2 m

For X>2 m,F=ve
i.e., displacement is in positive direction and force is negative. Therefore X=2 is a stable equilibrium position.

For X<2 m,F=ve
i.e., force and displacement are in negative directions. Therefore X=2 is an unstable equilibrium position.


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