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

A spring of spring constant $5 \times 10^3\, N/m$ is stretched initially by $5\,cm$ from the unstretched position. Then the work required to stretch it further by another $5\, cm$ is .............. $\mathrm{N}$  $-$ $\mathrm{m}$

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $ac$ is varying with time t as $a_c = k^2rt^2$ where $k$ is a constant. The power delivered to the particle by the force acting on it

A sphere of mass $m$ travelling at constant speed $v$ strike another sphere of same mass. If  coefficient of restitution is $e$, then ratio of velocity of both spheres just after collision is :-

A particle moves along the $x-$ axis from $x = 0$ to $x = 5\,m$ under the influence of a force $F$ (in $N$ ) given by $F = 3x^2 -2x + 7$ . Calculate the work done by this force .............. $\mathrm{J}$