$A$ body of mass $5 \times 10^{3} \, kg$ moving with speed $2 \, m/s$ collides with a body of mass $15 \times 10^{3} \, kg$ inelastically and sticks to it. The loss in $K.E.$ of the system will be (in $kJ$):

$A$ particle of mass $m$ moving in the $x$-direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$-direction with speed $v$. If the collision is perfectly inelastic,the percentage loss in the energy during the collision is close to .............. $\%$

$A$ 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 $m/s$?

$A$ bag of mass $M$ is suspended by a long string. $A$ bullet of mass $m$ moving with velocity $v$ hits the bag and gets embedded in it. For the (bag + bullet) system:

In a perfectly inelastic collision,what happens to the two colliding particles after the collision?

$A$ block of mass $4 m$ travelling at a velocity $v_1$ in the $x$-direction on a frictionless horizontal plane makes a head-on collision with another block of mass $2 m$ travelling in the opposite direction with a velocity $v_2$. After the collision,both blocks travel as a single block along the $x$-direction with a final velocity $5 v_2$. The ratio of velocities $\frac{v_1}{v_2}$ is