State the reason for the following:
$(i)$ Some leaves may get detached from a tree if we vigorously shake its branch.
$(ii)$ It is advised to tie any luggage kept on the roof of a bus with a rope.

$(a)$ State Newton's second law of motion. Use this law to find a method to measure force acting on an object.
$(b)$ From a rifle of mass $4 \ kg$,a bullet of mass $50 \ g$ is fired horizontally with an initial velocity of $40 \ m \ s^{-1}$. Calculate the initial recoil velocity of the rifle.

Amar, Javed, and Rita were riding in a bus that was moving with a high velocity on a highway when a bug hit the windshield and its dead body got stuck on the windscreen. Amar and Javed began discussing the situation. Amar suggested that the change in momentum of the bug is much greater than that of the bus. After all, argued Amar, there was no noticeable change in the velocity of the bus compared to the obvious change in the velocity of the bug. Javed opined that since the bus was moving with a larger velocity, so it exerted a larger force on the bug, as a result of which it died. Rita disagreed entirely, arguing that both the bug and bus experienced the same force and a change in their momentum. Who do you agree with? Support your answer.

$A$ sledge of mass $80 \, kg$ moves over the frozen surface of a lake with a velocity of $30 \, m s^{-1}$ and comes to rest in $5 \, s$. Find its negative acceleration and the frictional force between the lake and the sledge.

The acceleration of a body is to be doubled from its initial value. By what factor is the acting force to be increased?

What are the changes possible on an object at rest if we apply on it:
$(a)$ a balanced force?
$(b)$ an unbalanced force?