$A$ particle of mass $m$ moving with velocity $\vec{v_1}$ undergoes a two-dimensional elastic collision with another particle of mass $m$ at rest. If the particles move with velocities $\vec{v_1}'$ and $\vec{v_2}'$ after the collision,what is the angle between them in degrees?

$A$ body of mass $1\,kg$ collides head-on elastically with a stationary body of mass $3\,kg$. After the collision,the smaller body reverses its direction of motion and moves with a speed of $2\,m/s$. The initial speed of the smaller body before the collision is $..........\,m/s$.

Consider an elastic collision of a particle of mass $m$ moving with velocity $u$ with another particle of the same mass $m$ at rest. After the collision, the particles move at angles $\theta_1$ and $\theta_2$ with respect to the initial direction of motion. What is the sum of the angles $\theta_1 + \theta_2$ in degrees?

$A$ heavy body moving with a velocity of $6\,ms^{-1}$ collides elastically with a light body (whose mass is half of the mass of the heavy body) at rest. The velocity of the light body will be (in $ms^{-1}$):

As shown in the figure,a pendulum $A$ is released from an angle of $30^{\circ}$ with the vertical and strikes a pendulum $B$ of equal mass. After the collision,to what height (in $m$) will pendulum $A$ rise? Neglect the size of the pendulum and assume the collision is perfectly elastic.

$A$ smooth sphere $A$ is moving on a frictionless horizontal plane with angular speed $\omega$ and center of mass with velocity $v$. It collides elastically and head-on with an identical sphere $B$ at rest. Neglect friction everywhere. After the collision,their angular speeds are $\omega_A$ and $\omega_B$ respectively. Then