$A$ metal ball of mass $2 \,kg$ moving with a speed of $10 \,ms^{-1}$ has a head-on collision with a stationary ball of mass $3 \,kg$. If after the collision, both the balls move together, then the loss in kinetic energy due to the collision is: (in $\,J.$)

$A$ 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 $3 \ kg$ moving with a velocity $(2 \hat{i}+3 \hat{j}+3 \hat{k}) \ m/s$ collides with another body of mass $4 \ kg$ moving with a velocity $(3 \hat{i}+2 \hat{j}-3 \hat{k}) \ m/s$. The two bodies stick together after collision. The velocity of the composite body is

$A$ bullet of mass $m$ moving horizontally with speed $v_0$ hits a wooden block of mass $M$ that is suspended from a massless string. The bullet gets lodged into the block. If the block-bullet system swings to a maximum height $h$,how much of the initial kinetic energy of the bullet is lost in the collision?

$A$ body of mass $2 \, kg$ is moving with velocity $10 \, m/s$ towards the east. Another body of the same mass and same velocity moving towards the north collides with the former,coalesces,and moves towards the north-east. What is its final velocity?

$A$ mass of $20\, kg$ moving with a speed of $10\, m/s$ collides with another stationary mass of $5\, kg$. As a result of the collision,the two masses stick together. The kinetic energy of the composite mass will be ............. $J$.