$A$ 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?

$A$ 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

$A$ bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be

Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the minimum speed required to make both the blocks melt completely, if the initial temperatures of the blocks were $-8^{\circ} C$ each (in $ms^{-1}$)? (Specific heat of ice is $2100 \ Jkg^{-1} K^{-1}$ and latent heat of fusion of ice is $3.36 \times 10^{5} \ Jkg^{-1}$)

$A$ block of mass $m$ moving along a straight line with constant velocity $3 \vec{V}$ collides with another block of the same mass at rest. They stick together and move with a common velocity. The common velocity is:

$A$ body of mass $2 \ kg$ moving with a velocity of $3 \ m/s$ collides head-on with a body of mass $1 \ kg$ moving with a velocity of $4 \ m/s$ in the opposite direction. After the collision,the two bodies stick together and move with a common velocity: