A body of mass $1\,kg$ collides head on elastically with a stationary body of mass $3\,kg$. After 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 collision is $..........ms ^{-1}$

In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:

An inelastic ball is dropped from a height of $100\, m$. Due to earth$20\%$ of its energy is lost. To what height the ball will rise ......... $m$

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

Two billiard balls undergo a head-on collision. Ball $1$ is twice as heavy as ball $2$. Initially, ball $1$ moves with a speed $v$ towards ball $2$ which is at rest. Immediately after the collision, ball $1$ travels at $a$ speed of $v/3$ in the same direction. What type of collision has occured?

Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. They fly apart in opposite direction with equal speeds. If their masses are $m_A$ and $m_B$ respectively, then