Question

2 balls A and B of mass M and 2 m are in motion with velocities to 2v and V respectively compare their inertia, their Momentum and the force needed to stop them in the same time

Answer 1

Given:
Two balls A and B of mass m and 2m
Initial velocity of first ball =2V
Initial velocity of second ball= V
1)Compare inertia:
As inertia is measure of mass. Hence the object with greater mass has more mass.
So, Ball B is having more inertia.
2)Compare momentum:
Momentum is the product of mad and velocity.
P= mxv
So Pa=mx2v=2mv
Pb=2mxv=2mv
So, momentum in both the cases are same. 

3)The force needed to stop them in same time:
From Newton's second law:
F= dp/dt
= change in monentum/dt
= 0-2mv/time
As momentum is same for given time , so same force is required to stop them.

Answer 2

Inertia means which is directly proportional to mass. more the mass more is the inertia.Answer:

1.IA:IB=1:2
2.pA:pB=1:1 
3.FA:FB=1:1

Explanation:

Given that
Two balls are in motion:
A has mass m and velocity 2v
and 
B has mass 2m and velocity v
To do :
Compare :- 1. Their inertia 
2. Their momentum 
3. The force needed to stop them in the same time.

Step 1: As mass(m) is the measure of inertia(I)of any object,

Inertia of IAIB= m2m = 0.5 i.e. IA is half of IB

or we say IA:IB=1:2

Step 2: Momentum is given as p=mv

So momentum of A will be 
pA=m⋅2v = 2mv

And momentum of A will be 
pB=2m⋅v = 2mv

We find that the momentum of both the objects is same ,

so pA:pB=1:1

Step 3: F = rate of change of momentum =(m⋅vf−m⋅vi)/ t
where 
vf is final velocity,
vi is initial velocity and
t is the time taken.

The final momentum p in both the cases is zero as the object is to be stopped, i.e. velocity vf=0

F=m⋅vf−m⋅vit

FA=0−m⋅2vt = 2mvt

FB=0−2m⋅vt == 2mvt

As we need to stop both the balls in time is same , t will be same for both cases.

FA:FB=1:1

Answer :1. IA:IB=1:2
2. pA:pB=1:1 
3.FA:FB=1:1