A particle which is constrained to move along the x -axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin is F(x)=-k x+a x^3 . Here, k and a are positive constants. For x 0 , t

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A particle which is constrained to move along the x -axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin is F(x)=-k x+a x^3 . Here, k and a are positive constants. For x 0 , the functional from of the potential energy U_ (x) of the particle is

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Correct answer: 3

aligned & We know F=- d U d x & d U=-F d x & U=- ₀^x (-k x+a x^3 ) d x U= k x^2 2 - a x^4 4 & We get U=0 at x=0 and x= 2 k a & Also we get U= negative for x 2 k a aligned From the given function we can see that F=0 at x=0 i.e., slope of U-x graph is zero at x=0 .

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