A ball of mass $M$ falls from a height $h$ on a floor. If co-efficient of restitution is $e$, the height attained by the ball after two rebounds is

If $F = 2x^2 -3x -2$, then choose correct option

A stone tied to a string $L$ is whirled in a vertical circle, with the other end of the string at the centre. At a certain instant of time, the stone is as its lowest position and has a speed $u$. the magnitude of the change in its velocity as it reaches a position where the string is horizontal is

A force acts on a $3\, gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t -4t^2 + t^3$ , where $x$ is in $meters$ and $t$ is in $seconds$ . The work done during the first $4\, second$ is ................. $\mathrm{mJ}$

A particle moves along $x$-axis from $x=0$ to $x=5$ metre under the influence of a force $F=7-2 x+3 x^2$. The work done in the process is .............

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 .............. $\mathrm{N}$  $-$ $\mathrm{m}$