Question

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

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

From the equation, $F=-\frac{d U}{d x}$
$\displaystyle \int _{ \, 0}^{ \, U \left(x\right)} d U=-\displaystyle \int _{ \, 0}^{ \, x} F d x=-\displaystyle \int _{ \, 0}^{ \, x} \left(K x\right) d x$
$\therefore U \, \left(x\right)=-\frac{k x^{2}}{2}$
as $U \, \left(0\right)= \, 0$