Elastic And Inelastic Collision - Practice Questions & MCQ

• In Perfectly Elastic Collision, 

Law of conservation of momentum and that of Kinetic Energy hold good.

                         …….(1)

                                       …….(2)

From equation (1) and (2) 

                      We get,    …..(3)

                      Or,  we can say Relative velocity of approach = Relative velocity of separation 

And 

So in Perfectly Elastic Collision  

                                                                    e = 1 , 

                     From equations (1),(2), (3)

                     We get

                                            ……(4) 

                    Similarly,        ...... (5) 

•  Special cases of head on elastic collision 

1. Equal mass in case of perfectly elastic collision

Then, 

Or, Velocity mutually interchange

2.  If massive projectile collides with a light target  (i.e )

Since   so we use 

Putting in equation (4) and (5) 

We get

3. If target particle is massive in case of elastic collision  (i.e; )

Since  

So, the lighter particle recoil with same speed and the massive target particle remain practically at rest.

i.e;  

• Let two bodies moving as shown in figure.

By law of conservation of momentum

Along x-axis-

….. (1)

Along y-axis-

                            …..(2)

By law of conservation of kinetic energy

                              ….(3)

And In Perfectly Elastic Oblique Collision

Value of e=1 

So along line of impact (here along in the direction of )

We apply e=1 

And  we get      ….. (4)

So we solve these  equations (1),(2),(3),(4) to get unknown.

• Special condition

Then, from equation (1), (2) and (3)

We get,  

i.e; after perfectly elastic oblique collision of two bodies of equal masses (if the second body is at rest), the scattering angle    would be  .

1. In Inelastic Collision Law of conservation of momentum hold good but kinetic energy is not conserved .

                                        …… (1) 

2. In inelastic collision  (0 < e < 1)

            ….. (2)

From equations (1),(2) 

We get,

                 ……(3) 

Similarly,  ...... (4) 

3.  Special case

 A sphere of mass m moving with velocity u hits inelastically with another stationary sphere of same mass.

As,  

So,      or,                      ....(5) 

By conservation of momentum 

As,    

So                                                           ….(6)

From equation (5) and (6)

We get,  

4. Loss in kinetic energy

Loss in K.E =  Total initial kinetic energy – Total final kinetic energy

…. (7)

From equation (3) , (4) and (7)

We can write, Loss in kinetic energy in terms of e as

In Perfectly Inelastic Collision -  Two bodies stick together after the collision ,so there will be a final common velocity (v)

1. When the colliding bodies are moving in the same direction

• By the law of conservation of momentum 

• Loss in kinetic energy

2. When the colliding bodies are moving in the opposite direction

• By the law of conservation of momentum 

If v is positive then the combined body will move along the direction of motion of mass

If v is negative then the combined body will move in a direction opposite to the motion of mass

• Loss in kinetic energy

A block of mass M suspended by vertical thread.

A bullet of mass m is fired horizontally with velocity u in the block.

Let after the collision bullet gets embedded in block.

And, the combined system raised upto height h where the string makes an angle   with the vertical. 

1. Common velocity of system just after the collision (V)

Here, system is (block + bullet) 

                                                              .....(1)

2. Initial velocity of the bullet in terms of h

By the conservation of mechanical energy

3. Loss in kinetic energy

Loss of kinetic energy in perfectly inelastic collision when  is given by

4. Value of angle