For inelastic collision between two spherical rigid bodies

A ball of mass $'m'$ moving with a speed $'u'$ under goes a head-on elastic collision with a ball of mass $(nm)$  initially at rest. The fraction of the incident energy transferred to the heaveir ball is

Consider elastic collision of a particle of mass $m $ moving with a velocity $u$ with another particle of the same mass at rest. After the collision the projectile and the struck particle move in directions making angles ${\theta _1}$and ${\theta _2}$respectively with the initial direction of motion. The sum of the angles. ${\theta _1} + {\theta _2},$ is......$^o$

A ball of mass $200\,g$ rests on a vertical post of height $20\,m$. A bullet of mass $10\,g$, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of initial velocity of the bullet will be $............m/s$ (if $\left.g =10 m / s ^2\right)$

A body falling from a height of $10\,m$ rebounds from hard floor. If it loses $20\%$ energy in the impact, then coefficient of restitution 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