$A$ metal ball of mass $2 \,kg$ moving with a velocity of $36 \,km/h$ has a head-on collision with a stationary ball of mass $3 \,kg$. If after the collision,the two balls move together,the loss in kinetic energy due to the collision is ........ $J$.

$A$ body of mass $5\,kg$ strikes another body of mass $2.5\,kg$ initially at rest. The bodies after collision coalesce and begin to move as a whole with a kinetic energy of $5\,J$. The kinetic energy of the first body before collision is ............... $J$.

Two putty balls of equal mass $m$ moving with equal velocity $v = 45\sqrt{2} \, m/s$ in mutually perpendicular directions,stick together after collision. The velocity of their combined mass after collision is .................. $m/s$.

Two identical masses $M$ moving with velocities $\mu_1$ and $\mu_2$ collide perfectly inelastically. The loss in energy is

Two bodies of the same mass $m$ are moving with the same speed $v_0$,but in different directions in a plane. They undergo a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degrees) is:

$A$ 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