$A$ jet engine works on the principle of Newton's:

$A$ man throws a ball of mass $0.5\, kg$ vertically upward with a velocity of $25\, m s^{-1}$. Find:
$(a)$ The initial momentum of the ball.
$(b)$ The momentum of the ball at the halfway mark of the maximum height (given $g = 10\, m s^{-2}$).

What is the effect of force when it is applied in the following cases?
$(a)$ $A$ balloon is pressed from opposite sides.
$(b)$ $A$ ball is hit with a bat.
$(c)$ $A$ spring is compressed.

Which would require a greater force $-$ accelerating a $1\, kg$ mass at $10\, m s^{-2}$ or a $2\, kg$ mass at $4\, m s^{-2}$?

$(a)$ 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.

Prove that $1 \text{ N} = 10^{5} \text{ dynes}$.