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Question

# Potential energy of a particle moving along x− axis is given by U=(x33−4x+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 mU=x33−4x+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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