A)
B)
C)
D)
Correct Answer: D
Solution :
Given, \[F=kx\]where k is positive constant. Force, \[F=\frac{-dU(x)}{dx}\] or \[\frac{dU(x)}{dx}=-k\,x\] or \[dU(x)=-kx\,\,dx\] Integrating both the sides, \[U(x)=-\int_{{}}^{{}}{kx\,dx=-\frac{1}{2}}\,k{{x}^{2}}\] or \[{{x}^{2}}=-\frac{2}{k}U(x)\] ?(i) Comparing Eq. (i) with the standard equationof parabola, which is given by \[{{x}^{2}}=4ay\] we conclude that the graph of \[U(x)\]versus \[x\]satisfies the graph of parabola. Since the equation (i) has minus sign,therefore the graph will be open downwardsalong \[U(x).\]You need to login to perform this action.
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