The potential energy of a conservative system is given by U=Ax2−Bx, where x represents the position of the particle. A and B are positive constants. Then
A
Force acting on the system will be (B−2Ax)
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B
At equilibrium, potential energy will be −B24A
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C
system is in stable equilibrium.
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D
None
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Solution
The correct option is C system is in stable equilibrium. Given U=Ax2−Bx F=−dUdx=−(2Ax−B)=B−2Ax
At equilibrium, F=0=B−2Ax x=B2A, d2Udx2=2A=+ve, hence stable equilibrium. Potential energy at equilibriumU=A×B24A2−B×B2A=−B24A