Identify the type of collision for the following cases:
$(a)$ Collision between a negatively charged object and a positively charged object.
$(b)$ Collision between two very large objects.
$(c)$ Collision between two quartz balls.

$A$ ball of mass $0.2 \ kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2 \ m$ while applying the force and the ball goes up to $2 \ m$ height further,find the magnitude of the force $F$ in $N$. (Consider $g = 10 \ m/s^2$)

Two bodies $A$ and $B$ of masses $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring. $A$ third body $C$ of mass $m$ moves with velocity $V_0$ along the line joining $A$ and $B$ and collides elastically with $A$ as shown in the figure. At a certain instant of time $t_0$ after the collision,it is found that the instantaneous velocities of $A$ and $B$ are the same. Further,at this instant,the compression of the spring is found to be $x_0$. Determine the spring constant $k$.

$A$ dumbbell consisting of two masses $m$ each,connected by a light rigid rod of length $l$,falls from a height $h$ onto two pads of equal height,one steel and the other brass. The coefficients of restitution are $e_1$ and $e_2$ $(e_1 < e_2)$. To what maximum height will the centre of mass of the dumbbell rise after bouncing off the pads?

Two particles,of masses $M$ and $2M$,moving as shown,with speeds of $10\, m/s$ and $5\, m/s$,collide elastically at the origin. After the collision,they move along the indicated directions with speeds $v_1$ and $v_2$ respectively. The values of $v_1$ and $v_2$ are nearly:

$A$ bullet of mass $m$ moving with velocity $v_1$ strikes a wooden block of mass $M$ suspended as shown in the figure and gets embedded in it. If the block rises to a height $h$,what is the initial velocity of the bullet?