$A$ $50\, g$ bullet moving with velocity $10\, m/s$ strikes a block of mass $950 \,g$ at rest and gets embedded in it. The loss in kinetic energy will be ............... $\%$

$A$ body of mass $3 \,kg$ is moving with a velocity of $8 \,ms^{-1}$ collides head-on with another body of mass $1 \,kg$, moving in the opposite direction with a velocity of $4 \,ms^{-1}$. After the collision, if the two bodies stick together and move, they move with a common velocity: (in $\,ms^{-1}$)

$A$ 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 $\,cm$)

In a one-dimensional collision, a particle of mass $2m$ collides with a particle of mass $m$ at rest. If the particles stick together after the collision, what fraction of the initial kinetic energy is lost in the collision?

In a perfectly inelastic collision,what happens to the two colliding particles after the collision?

$A$ particle of mass $m$ moving eastward with a speed $v$ collides with another particle of the same mass moving northwards with the same speed $v$. The two particles coalesce on collision. The new particle of mass $2m$ will move with velocity: