The work done by the force $\vec{F} = x^2 \hat{i} + y^2 \hat{j}$ around the closed path $OABC$ shown in the figure 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 ................ $m/s$.

$Assertion$ : Frictional forces are conservative forces.
$Reason$ : Potential energy can be associated with frictional forces.

$A$ particle is acted upon by a force given by $F=-\alpha x^3-\beta x^4$,where $\alpha$ and $\beta$ are positive constants. At the point $x=0$,the particle is

If potential energy is given by $U = \frac{a}{r^2} - \frac{b}{r}$,find the maximum force. (Given $a = 2, b = 4$)

$A$ particle is released from rest at the origin. It moves under the influence of a potential field $U = x^2 - 3x$. The kinetic energy at $x = 2$ is ............... $J$.