A moving particle of mass $m,$ makes a head on elastic collision with another particle of mass $2\,m,$ which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to .................. $\%$

A rubber ball is dropped from a height of $5 \,m$ on a planet where the acceleration due to gravity is not known. On bouncing, it rises to $1.8\, m$. The ball loses its velocity on bouncing by a factor of

An alpha-particle of mass $m$ suffers $1-$ dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, $64\%$ of its initial kinetic energy. The mass of the nucleus is .......... $\mathrm{m}$

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 $2t_0$ while still moving in air. The value of $\left| {\left( {{m_1}{{\vec v}_1}' + {m_2}{{\vec v}_2}'} \right) - \left( {{m_1}{{\vec v}_1} + {m_2}{{\vec v}_2}} \right)} \right|$ is

Three particles $A, B$ & $C$ of equal mass move with speed $V$ as shown to strike at  centroid of equilateral triangle after collision. $A$ comes to rest & $B$ retraces its path  with speed $V$. speed of $C$ after collision is :-

The bob $A$ of a pendulum released from horizontal to the vertical hits another bob $B$ of the same mass at rest on a table as shown in figure.

If the length of the pendulum is $1\,m$, calculate

$(a)$ the height to which bob $A$ will rise after collision.

$(b)$ the speed with which bob $B$ starts moving.

Neglect the size of the bobs and assume the collision to be elastic.