A body of mass $m$  moving with velocity $v$ collides head on with another body of mass $2m $ which is initially at rest. The ratio of K.E. of colliding body before and after collision will be

As per the given figure, a small ball $P$ slides down the quadrant of a circle and hits the other ball $Q$ of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball $Q$ after collision will be $............\,m/s$ $:\left( g =10\,m / s ^2\right)$

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

Two identical balls $P$ and $Q$ moving in the $x-y$ plane collide at the origin $(x=0,y=0)$ of the coordinate system. Their velocity components just before the moment of impact were, for ball $P$, $v_x=6\ m/s$, $v_y=0$; for ball $Q$, $v_x=-5\ m/s$, $v_y=2\ m/s$. As a result of the collision, the ball $P$ comes to rest. The velocity components of the ball $Q$ just after collision will be

Two particles of masses ${m_1}$ and ${m_2}$ in projectile motion have velocities ${\vec v_1}$ and ${\vec v_2}$ respectively at time $t = 0$. They collide at time ${t_0}$. Their velocities become ${\vec v_1}'$ and ${\vec v_2}'$ at time $2{t_0}$ while still moving in air. The value of $|({m_1}\overrightarrow {{v_1}} '\, + {m_2}\overrightarrow {{v_2}} ') - ({m_1}\overrightarrow {{v_1}} \, + {m_2}\overrightarrow {{v_2}} )$| is

A ball hits the floor and rebounds after inelastic collision. In this case