A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ $meter$ as shown in figure. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ............. $\mathrm{m}/ \mathrm{s}$

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

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

A ball is dropped from height $h$ on a plane. If the coefficient of restitution of the plane is $e$ and if ball hits ground two times, the height upto which it reaches after two jumps, will be

A body is dropped from a height $h$ . If it acquires a momentum $p$ just before striking the ground, then the mass of the body is

A particle fall from height $h$ on $a$ static horizontal plane rebounds. If $e$ is coefficient of  restitution then before coming to rest the total distance travelled during rebounds will  be:-