Two bodies $A$ and $B$ of same mass undergo a completely inelastic one-dimensional collision. The body $A$ moves with velocity $v_1$ while body $B$ is at rest before the collision. The velocity of the system after the collision is $v_2$. The ratio $v_1: v_2$ is

$A$ body of mass $4\, kg$ moving with velocity $12\, m/s$ collides with another body of mass $6\, kg$ at rest. If two bodies stick together after collision,then the loss of kinetic energy of the system is .............. $J$.

$A$ mass $m$ moving horizontally (along the $x-$axis) with velocity $v$ collides and sticks to a mass of $3m$ moving vertically upward (along the $y-$axis) with velocity $2v$. The final velocity of the combination is

$A$ 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 $..........\%$

$A$ particle of mass $m_1$ moving with a velocity of $5 \ m/s$ undergoes a head-on collision with a stationary particle of mass $m_2$. After the collision,both particles move with a common velocity of $4 \ m/s$. Find the ratio $m_1/m_2$.

Ball $A$ of mass $1 \,kg$ moving along a straight line with a velocity of $4 \,ms^{-1}$ hits another ball $B$ of mass $3 \,kg$ which is at rest. After collision, they stick together and move with the same velocity along the same straight line. If the time of impact of the collision is $0.1 \,s$, then the force exerted on $B$ is (in $\,N$)