The variation of force $F$ acting on a body moving along $x$-axis varies with its position $(x)$ as shown in figure The body is in stable equilibrium state at

Figure shows the vertical section of frictionless surface. $A$ block of mass $2\, kg$ is released from the position $A$ ; its $KE$ as it reaches the position $C$ is ................ $\mathrm{J}$

A body constrained to move along $y-$ axis is subjected to a constant force $\vec F =  - \hat i + 2\hat j + 3\hat k\,N$ The work done by this force in moving the body a distance of $4\, m$ along $y-$ axis is ............... $\mathrm{J}$

In an elastic collision of two particles the following quantity is conserved

$ABCDE$ is a channel in the vertical plane, part $BCDE$ being circular with radius $r$ . A block is released from $A$ and slides without friction and without rolling. The block will complete the loop if $h$ is

The work done by a force $\vec F\, = \,( - \,6{x^3}\,\hat i)N$ , in displacing a particle from $x = 4\,m$ to $x = -\,2\,m$ is .............. $\mathrm{J}$