$A$ bullet of mass $10 \, g$ is fired with a velocity of $400 \, m s^{-1}$ from a gun of mass $4 \, kg$. What is the recoil velocity of the gun (in $, m s^{-1}$)?

How would you arrive at a mathematical formula to measure force using the second law of motion?

$(a)$ 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.

Explain the following:
$(i)$ Why is it difficult to walk on marshy land?
$(ii)$ Why does an air-filled balloon rise up slightly when punctured from below?
$(iii)$ Why does a swimmer push water backward with his hands in order to swim in the forward direction?

$(a)$ Define inertia. There are three solid balls, made of aluminium, steel, and wood, of the same shape and volume. Which of them would have the highest inertia? Why?
$(b)$ Describe in brief an activity to illustrate the property of inertia of rest.

$A$ man is at rest in the middle of a pond on perfectly smooth ice. He can get himself to the shore by making use of Newton's: