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.

To maintain a speed of $80\,km/h$ by a bus of mass $500\,kg$ on a plane rough road for $4\,km$ distance,the work done by the engine of the bus will be $........\,kJ$. [The coefficient of friction between the tyre of the bus and the road is $0.04$].

$A$ block of mass $m = 5 \text{ kg}$ is released from the top of an inclined plane as shown in the figure. The inclined plane has a length of $10 \text{ m}$ and an angle of $30^{\circ}$. The horizontal surface has a coefficient of kinetic friction $\mu = 0.5$ and a length of $2 \text{ m}$ before the spring of spring constant $k = 100 \text{ N/m}$. Calculate the maximum compression $x$ in the spring.

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

$A$ rain drop of radius $2 \; mm$ falls from a height of $500 \; m$ above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height,it attains its maximum (terminal) speed,and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is $10 \; m s^{-1}$?

The friction coefficient between the horizontal surface and each of the blocks shown in the figure is $\mu = 0.2$. The collision between the blocks is perfectly elastic. What is the separation between the blocks when they come to rest? (in $cm$)