$A$ 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 $m_1/m_2$.

$A$ particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2m$ and sticks to it. What will be the speed of the system?

$A$ 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 $...... \ J$.

$A$ particle of mass $m$ moves with velocity $v$ towards the East. It collides with another particle of the same mass and same speed moving towards the North and sticks to it. What will be the velocity of the combined particles?

$A$ bag of sand of mass $9.8 \, kg$ is suspended by a rope. $A$ bullet of mass $200 \, g$ travelling with a speed of $10 \, ms^{-1}$ gets embedded in it. The loss of kinetic energy 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 ................ $cm$.