A particle is made to move from the origin in three spells of equal distances, first along the $x-$ axis, second parallel to $y-$ axis and third parallel to $z-$ axis. One of the forces acting on it is has constant magnitude of $50\,N$ and always acts along the direction of motion. Work done by this force in the three spells of motion are equal and total work done in all the three spells is $300\,J$. The final coordinates of the particle will be

$A$ particle of mass $m$ is released from $a$ height $H$ on $a$ smooth curved surface which ends into a vertical loop of radius $R$, as shown The minimum value of $H$ required so that the particle makes a complete vertical circle is given by

A body of mass $m$ is projected from ground with speed $u$ at an angle $\theta$ with horizontal. The power delivered by gravity to it at half of maximum height from ground is

Work equal to $25\,J$ is done on a mass of $2\,kg$ to set it in motion. If whole of it is used to increase the kinetic energy then velocity acquired by the mass is ............ $\mathrm{m}/ \mathrm{s}$

A body moving with speed $v$ in space explodes into two piece of masses in the ratio $1 : 3.$ If the smaller piece comes to rest, the speed of the other piece is

A rope is used to lower vertically a block of mass $M$ by a distance $x$ with a constant downward acceleration $\frac{g}{2}$. The work done by the rope on the block is