Two identical bullets are fired,one by a light rifle and another by a heavy rifle with the same force. Which rifle will hurt the shoulder more and why?

Using the second law of motion,derive the relation between force and acceleration. $A$ bullet of $10 \, g$ strikes a sandbag at a speed of $10^3 \, m \, s^{-1}$ and gets embedded after traveling $5 \, cm$. Calculate:
$(i)$ The resistive force exerted by the sand on the bullet.
$(ii)$ The time taken by the bullet to come to rest.

Calculate the ratio of momentum,when
$(i)$ velocity of an object is doubled.
$(ii)$ mass of an object is halved.
$(iii)$ both mass and velocity are increased by three times.

In the following table,the mass and speed of two bodies are given. Which body has more momentum? Justify your answer.

Body	Mass $(kg)$	Speed $(m s^{-1})$
$A$	$1$	$10$
$B$	$2$	$9$

Kicking a football requires less force than kicking a basketball. Why?

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.