A body of mass $5\, kg$ moving with a velocity $10\,m/s$ collides with another body of the mass $20 \,kg$ at, rest and comes to rest. The velocity of the second body due to collision is ......... $m/s$

In the figure shown, a small ball hits obliquely a smooth and horizontal surface with speed $u$ whose $x$ and $y$ components are indicated. If the coefficient of restitution is $\frac{1}{2}$, then its $x$ and $y$ components $v_x$ and $v_y$ just after collision are respectively

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

Three blocks are initially placed as shown in the figure. Block $A$ has mass $m$ and initial velocity $v$ to the right. Block $B$ with mass $m$ and block $C$ with mass $4m$ are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block $A$ is

A mass of $20\, kg$ moving with a speed of $10\,m/s$ collides with another stationary mass of $5\,kg.$ As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be ............. $J$

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of ${A}, {B}$ and ${C}$ are ${m}, 2\, {m}$ and $2\, {m}$ respectively. $A$ moves towards ${B}$ with a speed of $9$ ${m} / {s}$ and makes an elastic collision with it. Thereafter $B$ makes a completely inelastic collision with $C.$ All motions occur along same straight line. The final speed of $C$ is $....\,{m} / {s}$