A body of mass $2\, {kg}$ moving with a speed of $4\, {m} / {s}$. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $\frac{x}{10} \,{m} / {s}$. Then the value of $x$ is ..... .

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

Two identical balls $A$ and $B$ having velocities of $0.5\, m s^{-1}$ and $-0.3 \, m s^{-1}$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be

A mass of $20\, kg$ moving with a speed of $10\,m/s$ collides with another stationary mass of $5\,kg.$ As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be ............. $J$

A proton of mass $m$ collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of $90^o$ with respect to each other. The mass of unknown particle is

A ball of mass $1\,\,kg.$  moving with a velocity of $4\,\,m/sec.$  collides with a stationary ball. The collision is oblique. After the collision the first moves at right angle to its, initial direction with a velocity of  $3\,\,m/s.$  The momentum of the second ball (in $kg.\,\,m/s.$ ) after collision would be nearly