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=2m and x=−2m
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B
x=−2m and x=2m
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C
x=0 and x=0
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D
x=1m and x=−1m
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Solution
The correct option is Ax=2m and x=−2m U=x33−4x+6 F=−dUdx=−x2+4 ⇒F=0 at x=±2m
For X>2m,F=−ve
i.e., displacement is in positive direction and force is negative. Therefore X=2 is a stable equilibrium position.
For X<−2m,F=−ve
i.e., force and displacement are in negative directions. Therefore X=−2 is an unstable equilibrium position.