An unknown nucleus of mass $m_1$ collides with a stationary ${}^4He$ nucleus of mass $m_2$. After the collision,the two nuclei travel in perpendicular directions relative to each other. If kinetic energy is lost in the collision,the unknown nucleus must be:

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 $10^{\circ}$ 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.

Two bodies having same mass $40\, kg$ are moving in opposite directions,one with a velocity of $10\, m/s$ and the other with $7\, m/s$. If they collide and move as one body,the velocity of the combination is ........ $m/s$.

$A$ ball is dropped from a height $h$. After it strikes the ground twice,what height will it reach?

$A$ ball of mass $m$ moving with velocity $v$ collides head-on with a second ball of mass $m$ at rest. If the coefficient of restitution is $e$,the velocity of the first ball after collision is $v_1$,and the velocity of the second ball after collision is $v_2$,then:

$A$ body falls on a surface with a coefficient of restitution of $0.6$ from a height of $1 \, m$. The body rebounds to a height of ........... $m$.