$A$ 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 $\,cm$)

$A$ 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 $... J$.

$A$ 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

$A$ bag of mass $M$ is suspended by a string. $A$ bullet of mass $m$ moving with velocity $v$ enters the bag and gets embedded in it. Then,for the system:

$A$ body of mass $1 \ g$ moving with a velocity of $3\hat{i} - 2\hat{j} \ m/s$ collides with a body of mass $2 \ g$ moving with a velocity of $4\hat{j} - 6\hat{k} \ m/s$. If the two bodies stick together after the collision,what is the magnitude of their combined velocity in $m/s$?

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