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 as F(x) = –kx + ax 3 . Here k and a are positive constants. For x 
0, the functional form of the potential energy U(x) of the particle is
Text Solution
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F = – 
dU = – F. dx or U(x) = – 
U(x) = 
– 
U(x) = 0 and x = 0 and x = 
U(x) = negative for x > 
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. Therefore, the most appropriate option is .
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