On a particle placed at origin a variable force F=-a x (where a is a positive constant) is applied. If U(0)=0, the graph between potential energy of particle U(x) and x is best represented by

Question

On a particle placed at origin a variable force F=-a x (where a is a positive constant) is applied. If U(0)=0, the graph between potential energy of particle U(x) and x is best represented by (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

F=-a x=(-d U/d x) Integrating both sides U=(a x2/2)

Q. On a particle placed at origin a variable force $F = - a x$ (where $a$ is a positive constant) is applied. If $U (0) = 0$ , the graph between potential energy of particle $U (x)$ and $x$ is best represented by

$F = - a x = \frac{- d U}{d x}$
Integrating both sides
$U = \frac{a x ^{2}}{2}$

Q. On a particle placed at origin a variable force F=−ax (where a is a positive constant) is applied. If U(0)=0, the graph between potential energy of particle U(x) and x is best represented by

F=−ax=dx−dU​ Integrating both sides U=2ax2​

Q. On a particle placed at origin a variable force $F = - a x$ (where $a$ is a positive constant) is applied. If $U (0) = 0$ , the graph between potential energy of particle $U (x)$ and $x$ is best represented by

$F = - a x = \frac{- d U}{d x}$
Integrating both sides
$U = \frac{a x ^{2}}{2}$