State whether the following statement is true or false:
$1 \ N$ is the force that produces an acceleration of $1 \ m \ s^{-2}$ in a body of mass $1 \ g$.

Two cars each of mass $1000 \ kg$ are moving in a straight line but in opposite directions. The velocity of each car is $5 \ m s^{-1}$ before the collision during which they stick together. What will be the velocity of the combined cars after collision (in $m s^{-1}$)?

$(a)$ Two objects of masses $100\, g$ and $200\, g$ are moving along the same line and direction with velocities $2\, m s^{-1}$ and $1\, m s^{-1}$ respectively. They collide and after the collision,the first object moves at a velocity of $1.67\, m s^{-1}$. Determine the velocity of the second object.
$(b)$ If a man jumps out from a boat,the boat moves backwards. Why?

Explain the following:
$(i)$ Why does a boatman push the river bank backward with a long bamboo pole when launching his boat into the water?
$(ii)$ Why does a boat tend to leave the shore when passengers are alighting from it? How does the boatman overcome this difficulty?
$(iii)$ Why does a gun recoil when fired?
$(iv)$ How do rockets operate in space?

$(a)$ Name the force that keeps the object moving in a circular path with constant acceleration.
$(b)$ What would happen if this force is absent?

In the following cases,identify the direction of the net force acting on the objects:
$(a)$ $A$ car drives around a circular race track at a constant speed.
$(b)$ Earth moving around the sun.
$(c)$ $A$ ball,rolling across a grassy field,slowly comes to a stop.