$A$ body of mass $40\,kg$ having velocity $4\,m/s$ collides with another body of mass $60\,kg$ having velocity $2\,m/s$. If the collision is perfectly inelastic, then the loss in kinetic energy will be .............. $J$.

$A$ bullet weighing $10 \,g$ and moving with a velocity $300 \,m/s$ strikes a $5 \,kg$ block of ice and gets embedded in it. The ice block is kept on a smooth surface. The speed of the block after the collision is ........ $cm/s$.

$A$ particle of mass $m$ moving eastward with a speed $v$ collides with another particle of the same mass moving northward with the same speed $v$. The two particles coalesce on collision. The new particle of mass $2m$ will move in the north-easterly direction with a velocity

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

$A$ 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:

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