$A$ particle of mass $m$ moving with a velocity $\vec{V}$ makes a head-on elastic collision with another particle of the same mass initially at rest. The velocity of the first particle after the collision will be:

$A$ body of mass $m$ moving with velocity $v$ undergoes a head-on elastic collision with another body of mass $2m$ which is initially at rest. The ratio of the kinetic energy $(K.E.)$ of the colliding body before and after the collision is: (in $: 1$)

$A$ light particle moving horizontally with a speed $v_1$ strikes a very heavy block moving in the same direction with a speed $v_2$. The collision is elastic. After the collision,the velocity of the particle is:

$A$ truck moving on a horizontal road towards the east with a velocity of $20\, ms^{-1}$ collides elastically with a light ball moving with a velocity of $25\, ms^{-1}$ towards the west. What is the velocity of the ball just after the collision?

$A$ body of mass $m_1$ undergoes a perfectly elastic collision with a stationary body of mass $m_2$. If the velocity of mass $m_1$ becomes $1/1.5$ times its initial velocity,find the ratio $\frac{m_1}{m_2}$.

$A$ sphere $P$ of mass $m$ moving with velocity $v$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be .............. $^o$.