$A$ 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 $m_1/m_2$.

$A$ 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 ................ $cm$.

$A$ particle of mass $m$ moving in the $x$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$ direction with speed $v$. If the collision is perfectly inelastic,the percentage loss in the energy during the collision is close to $..........\%$

Velocity of the ball $A$ after collision with the ball $B$ as shown in the figure is ............. $m/s$. (Assume perfectly inelastic and head-on collision)

$A$ bag (mass $M$) hangs by a long thread and a bullet (mass $m$) comes horizontally with velocity $v$ and gets caught in the bag. Then for the combined (bag $+$ bullet) system

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 ......... $m/s$.