Question

4. Two objects of masses 100 g and
200 g are moving along the same
line and direction with velocities
of 2ms and Imst respectively.​

Answer 1

$\huge\bf\underline{\red{A}\green{N}\orange{S}\pink{W}\purple{E}\blue{R}}$

$\pink{▬▬▬}$$\red{▬▬▬}$$\green{▬▬▬}$$\blue{▬▬▬}$$\orange{▬▬▬}$

$\huge\bf\underline{\red{G}\green{i}\orange{v}\pink{e}\purple{n}\blue{:-}}$

Before Collision After collision

A B A B

100 g 200g → 100g 200g

2m/s 1m/s v=? 1.67ms

−1

$\huge\bf\underline{\red{E}\green{x}\orange{p}\pink{l}\purple{at}\blue{ion:-}}$

Let the 100 g and 200 g objects be A and B as shown in above figure.

Initial momentum of A=

1000

100

×2=0.2kgms

−1

Initial momentum of B=

1000

200

×1=0.2kgms

−1

∴ Total momentum of A and B before collision

=0.2+0.2=0.4kgms

−1

Let the velocity of A after collision =v

∴ Momentum of A after collision =

1000

100

×v=0.1v

Also, momentum of B after collision

=

1000

200

×1.67=0.334kgms

−1

∴ Total momentum of A and B after collision

=0.1×v+0.334

Using the law of conservation of momentum, momentum of A and B after collision = momentum of A and B before collision

0.1×v+0.334=0.4

0.1×v=0.4−0.334

⇒v=

0.1

0.066

=0.66ms

−1

$\pink{▬▬▬}$$\red{▬▬▬}$$\green{▬▬▬}$$\blue{▬▬▬}$$\orange{▬▬▬}$

Answer 2

Before Collision                   After collision

A                    B                   A                  B

100 g           200g    →    100g          200g

2m/s             1m/s               v=?           1.67m/s

Let the 100 g and 200 g objects be A and B as shown in above figure.

Initial momentum of A= 100 /1000  x 2 = 0.2kgm/s

Initial momentum of B= 200/1000 x 1 = 0.2kgm/s  

∴ Total momentum of A and B before collision

=0.2+0.2=0.4kgm/s

Let the velocity of A after collision =v

∴ Momentum of A after collision = 100/1000 x v = 0.1v

Also, momentum of B after collision

200/1000 x 1.67 = 0.334kgm/s

∴ Total momentum of A and B after collision

=0.1×v+0.334

Using the law of conservation of momentum, momentum of A and B after collision = momentum of A and B before collision

0.1×v+0.334=0.4

0.1×v=0.4−0.334

⇒v= 0.066/0.1 = 0.66m/s