$A$ clay ball of mass $m$ and speed $v$ strikes another metal ball of the same mass $m$,which is at rest. They stick together after the collision. The kinetic energy of the system after the collision is

$A$ body of mass $2 \, kg$ moving with a velocity $(\hat{i} + \hat{j} + \hat{k}) \, m/s$ collides with another body of mass $5 \, kg$ moving with velocity $(\hat{i} - 2\hat{j} + 3\hat{k}) \, m/s$. If they stick together, the velocity (in $m/s$) of the composite body is:

$A$ body of mass $20 \ kg$ moving with a speed of $10 \ m/s$ collides with a stationary body of mass $5 \ kg$. After the collision,both bodies stick together. The combined kinetic energy of the system will be $...... \ J$.

$A$ body of mass $1\,kg$ falls freely from a height of $100\,m$ onto a platform of mass $3\,kg$ which is mounted on a spring having spring constant $k = 1.25 \times 10^6\,N/m.$ The body sticks to the platform and the spring's maximum compression is found to be $x.$ Given that $g = 10\,m/s^2,$ the value of $x$ will be close to ................ $cm$.

$A$ mass $m$ moving horizontally (along the $x-$axis) with velocity $v$ collides and sticks to a mass of $3m$ moving vertically upward (along the $y-$axis) with velocity $2v$. The final velocity of the combination is

$A$ ball moving horizontally with a velocity $2 \,ms^{-1}$ strikes the bob of a seconds pendulum at rest. If the mass of the bob is equal to the mass of the ball and the collision is perfectly elastic, after collision the bob of the pendulum will raise to a height of $(g=10 \,ms^{-2})$ (in $\,cm$)