For a system of conservative forces,the potential energy $U$ is given by the formula $U = ax^2 - bx$,where $a$ and $b$ are constants. Determine the force $F$.

The potential energy of a particle varies with distance $x$ as shown in the graph. Select the wrong statement.

$A$ particle of mass $m$ with initial kinetic energy $K$ approaches the origin from $x = +\infty$. Assume that a conservative force acts on it and its potential energy $V(x)$ is given by $V(x) = \frac{K}{\exp(3x/x_0) + \exp(-3x/x_0)}$, where $x_0 = 1 \ m$. The speed of the particle at $x = 0$ is

$A$ particle moves in a one-dimensional field with total mechanical energy $E$. If the potential energy of the particle is $V(x)$,then:

The points of maximum and minimum attraction in the curve between potential energy $(U)$ and distance $(r)$ of a diatomic molecule are respectively:

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: In a central force field,the work done is independent of the path chosen.
Reason $R$: Every force encountered in mechanics does not have an associated potential energy.
In the light of the above statements,choose the most appropriate answer from the options given below: