A body of mass $5\,kg$ strikes another body of mass $2.5\,kg$ initially at rest. The bodies after collision coalesce and begin to move as a whole with a kinetic energy of $5\,J$. The kinetic energy of the first body before collision is ............... $\mathrm{J}$

A heavy steel ball of mass greater than $1\, kg$ moving with a speed of 2$m\,{\sec ^{ - 1}}$collides head on with a stationary ping-pong ball of mass less than $0.1\, gm$. The collision is elastic. After the collision the ping-pong ball moves approximately with speed ......... $m\,{\sec ^{ - 1}}$

A ball impinges directly on a similar ball at rest. If $1/4^{th}$ of the kinetic energy is lost by the impact, the value of coefficient of restitution is

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (figure). One of the bobs is released after being displaced by $10^o$ so that it collides elastically head-on with the other bob.

$(a)$ Describe the motion of two bobs.

$(b)$ Draw a graph showing variation in energy of either pendulum with time, for $0\, \leqslant \,t\, \leqslant \,2T$, where $T$ is the period of each pendulum.

Blocks of masses $m , 2 m , 4 m$ and $8 m$ are arranged in a line on a frictionless floor. Another block of mass $m ,$ moving with speed $v$ along the same line (see figure) ollides with mass $m$ in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8 m$ starts moving the total energy loss is $p \%$ of the original energy. Value of $'p'$ is close to

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