Question

two object of mases 100 g and 200 g moving along the same line and direction with velocitys 2m s-¹ and 1m s-¹ respectively they collide and after the collision ,the first object moves at a velocity 1.67 m s-¹. determine the velocity of the second object​

Answer 1

Given :

• Mass of the first object, $\sf\: m_{1}$ = 100 g

• Mass of the second object, , $\sf\: m_{2}$ = 200 g

• Initial velocity of the first object, , $\sf\: u_{1}$ = 2 ms-¹

• Initial velocity of the second object, $\sf\: u_{2}$ = 1 ms-¹

• Final velocity of the first object = 1.67 ms-¹

To Find :

• Final Velocity of the second object

Solution :

Calculation of momentum of first object :

★ Momentum = Mass × Velocity

→ Momentum = $\sf\dfrac{100}{1000}$ × 2

→ Momentum = 0.1 × 2

→ Momentum = 0.2 kg ms-¹

Calculation of momentum of second object :

★ Momentum = Mass × Velocity

→ Momentum = $\sf\dfrac{200}{1000}$ × 1

→ Momentum = 0.2 × 1

→ Momentum = 0.2 kg ms-¹

Now,

Total momentum before collision = 0.2 + 0.2 = 0.4 kg ms-¹

Calculation of final momentum of the first object :

★ Momentum = Mass × Velocity

→ Momentum = 0.1 × 1.67

→ Momentum = 0.167 kg ms-¹

Calculation of final momentum of the second object :

Let the final velocity of second object be v

→ Momentum = 0.2 × v

→ Momentum = 0.2v

So,

Total momentum after collision = 0.167 + 0.2v

According to law of conservation of momentum :

★ Total momentum before collision = Total momentum after collision

→ 0.4 = 0.167 + 0.2 v

→ 0.4 - 0.167 = 0.2v

→ 0.2v = 0.233

→ v = 1.165 ms-¹

$\therefore$ Final Velocity of the second object is 1.165 ms-¹.

Answer 2

Answer:

Given :

• Mass of the first object, \sf\: m_{1}m

1

= 100 g

• Mass of the second object, , \sf\: m_{2}m

2

= 200 g

• Initial velocity of the first object, , \sf\: u_{1}u

1

= 2 ms-¹

• Initial velocity of the second object, \sf\: u_{2}u

2

= 1 ms-¹

• Final velocity of the first object = 1.67 ms-¹

To Find :

• Final Velocity of the second object

Solution :

Calculation of momentum of first object :

★ Momentum = Mass × Velocity

→ Momentum = \sf\dfrac{100}{1000}

1000

100

× 2

→ Momentum = 0.1 × 2

→ Momentum = 0.2 kg ms-¹

Calculation of momentum of second object :

★ Momentum = Mass × Velocity

→ Momentum = \sf\dfrac{200}{1000}

1000

200

× 1

→ Momentum = 0.2 × 1

→ Momentum = 0.2 kg ms-¹

Now,

Total momentum before collision = 0.2 + 0.2 = 0.4 kg ms-¹

Calculation of final momentum of the first object :

★ Momentum = Mass × Velocity

→ Momentum = 0.1 × 1.67

→ Momentum = 0.167 kg ms-¹

Calculation of final momentum of the second object :

Let the final velocity of second object be v

→ Momentum = 0.2 × v

→ Momentum = 0.2v

So,

Total momentum after collision = 0.167 + 0.2v

According to law of conservation of momentum :

★ Total momentum before collision = Total momentum after collision

→ 0.4 = 0.167 + 0.2 v

→ 0.4 - 0.167 = 0.2v

→ 0.2v = 0.233

→ v = 1.165 ms-¹

\therefore∴ Final Velocity of the second object is 1.165 ms-¹.