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, $F=-\frac{dU}{dx}$
$\underset{0}{\overset{U\left(x\right)}{\int }}dU=-\underset{0}{\overset{x}{\int }}Fdx=-\underset{0}{\overset{x}{\int }}\left(Kx\right)dx$
$\therefore U\left(x\right)=-\frac{k{x}^2}{2}$
as $U\left(0\right)=0$