$A$ bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. What is conserved?

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

$A$ $50\, g$ 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 $m_1$ moving with a uniform velocity of $40 \, m/s$ collides with another mass $m_2$ at rest,and then the two together begin to move with a uniform velocity of $30 \, m/s$. The ratio of their masses $\frac{m_1}{m_2}$ is:

$A$ body of mass $5\,kg$ strikes another body of mass $2.5\,kg$ initially at rest. The bodies after collision coalesce and begin to move as a whole with a kinetic energy of $5\,J$. The kinetic energy of the first body before collision is ............... $J$.

$A$ 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