$A$ body of mass $m$ moves with velocity $v$ in the East direction,and another body of the same mass moves with velocity $v$ in the North direction. After they collide and stick together,what is the combined velocity of the resulting body of mass $2m$?

Two balls of masses $m$ each are moving at right angles to each other with velocities $6 \, m/s$ and $8 \, m/s$ respectively. If the collision between them is perfectly inelastic,the velocity of the combined mass is ......... $m/s$.

$A$ body of mass $m$ moving with a constant velocity $v$ hits another body of the same mass that is at rest. If the two bodies stick together after the collision,the velocity of the compound body 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 $\,cm$)

$A$ particle of mass $m_1$ moving with a velocity of $5 \ m/s$ undergoes a head-on collision with a stationary particle of mass $m_2$. After the collision,both particles move with a common velocity of $4 \ m/s$. Find the ratio $m_1/m_2$.

Statement $1$: In a perfectly inelastic collision,the total energy of two particles moving in the same direction is not completely lost.
Statement $2$: The principle of conservation of momentum is valid for all types of collisions.