A shell is fired from a canon with a velocity $V$ at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces come to rest. The speed of the other piece immediately after the explosion is

Ball $A$ moving at $12\ m/s$ collides elastically with $B$ at rest as shown. If both balls have the same mass, what is the final velocity of ball $A$ ? .................. $m/s$

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

If the momentum of a body increases by $0.01\%$, its kinetic energy will increase by ........... $\%$

A long spring, when stretched by a distance $x,$ has the potential energy $u.$ On increasing the stretching to $nx.$ The potential energy of the spring will be

Force acting on a particle moving in a straight line varies with the velocity of the particle as $F = \frac{K}{\upsilon }$  where $K$ is a constant. The work done by this force in time $t$ is