Two balls $A$ and $B$ of masses $m$ and $2m$ are in motion with velocities $2V$ and $V$ respectively. Compare:
$(i)$ their inertia,
$(ii)$ their momentum,and
$(iii)$ the force needed to stop them in the same time.

(A) $(i)$ Inertia of a body is directly proportional to its mass. Therefore,the ratio of inertia of ball $A$ to ball $B$ is $m : 2m = 1 : 2$.
$(ii)$ Momentum $p$ is defined as the product of mass and velocity $(p = mv)$. For ball $A$,$p_A = m \times 2V = 2mV$. For ball $B$,$p_B = 2m \times V = 2mV$. Thus,the ratio of their momentum is $2mV : 2mV = 1 : 1$.
$(iii)$ According to Newton's second law of motion,the force $F$ required to stop a body in a given time $t$ is $F = \frac{\Delta p}{t}$. Since both balls have the same initial momentum and are brought to rest (final momentum $= 0$) in the same time $t$,the change in momentum $\Delta p$ is the same for both. Therefore,the ratio of the force needed to stop them is $1 : 1$.