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 $A$ ? .................. $m/s$

The spacecraft of mass $M$ moves with velocity $V$ in free space at first, then it explodes breaking  into two pieces. If after explosion a piece of mass $m$ comes to rest, the other piece of space craft will have a velocity

The work done by a force $\vec F\, = \,( - \,6{x^3}\,\hat i)N$ , in displacing a particle from $x = 4\,m$ to $x = -\,2\,m$ is .............. $\mathrm{J}$

A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are

A body of mass $m$ moving with velocity $v$ collides head on with another body of mass  $2\, m$ which is initially at rest. The ratio of $K.E.$ of the colliding body before and  after collision will be 

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