1. Tardigrade
  2. Question
  3. Physics
  4. A particle is placed at the origin and a force F = kx is acting on it (where, k is a positive constant). If U (0) = 0 , the graph of U (x ) versus X will be, (where , U is the potential energy function)

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Q. A particle is placed at the origin and a force $F = kx$ is acting on it (where, $k$ is a positive constant). If $U (0) = 0 $, the graph of $U (x )$ versus $X$ will be, (where , $U$ is the potential energy function)

UPSEEUPSEE 2015

Solution:

From, $F=- \frac{d U}{d x}$
$ d U =-F \,d x $
$ U =\int_{0}^{u(x)} \,d U=-\int_{0}^{x} F d x $
$=-\int_{0}^{x} k x \,d x $
$ U =\frac{k x^{2}}{2} $
As, $U(0)=0, \alpha x^{2}$ (where $\alpha$ is a constant) and $U$ are negative.