In a gravitational field,if the work done along paths $1, 2$ and $3$ is ${W_1}, {W_2}$ and ${W_3}$ respectively,then:

Given below is the plot of a potential energy function $U(x)$ for a system,in which a particle is in one-dimensional motion,while a conservative force $F(x)$ acts on it. Suppose that $E_{\text{mech}} = 8 \, J$,the incorrect statement for this system is:

$A$ body with mass $2\, kg$ moves in one direction in the presence of a force which is described by the potential energy graph. If the body is released from rest at $x = 2\, m$,then its speed when it crosses $x = 5\, m$ is ................ $m/s$.

$A$ body falls towards the Earth in air. Will its total mechanical energy be conserved during the fall? Justify.

The potential energy for a conservative system is given by:
$U = ax^2 - bx$
Where $a$ and $b$ are positive constants. The law of the force governing the system is:

Which quantity is obtained by taking the negative derivative of potential energy with respect to displacement in the case of a conservative force?