# Momentum

## Numertical Problems

**Type I: (Calculation of Momentum)**

Question 1: What will be the momentum of a stone having mass of 10 kg when it is thrown with a velocity of 2m/s?

**Solution:** Given,

Mass (m) = 10kg

Velocity (v) = 2m/s

Momentum (p) =?

We know that, Momentum (p) = Mass (m) × Velocity (v)

Therefore, `p = 10kg xx 2 m//s = 20 kg m//s`

Thus the momentum of the stone `= 20 kg m//s`

Question 2: Calculate the momentum of a bullet of 25 g when it is fired from a gum with a velocity of 100m/s.

**Solution:**

Given, Velocity of the bullet (v) = 100m/s

Mass of the bullet (m) `= 25 g = 25/1000 kg = 0.025kg`

Momentum (p) =?

Or, `p = 2.5 kg m//s`

Thus the momentum of the bullet `= 2.5 kg m//s`

Question 3: Calculate the momentum of a bullet having mass of 25 g is thrown using hand with a velocity of 0.1 m/s.

**Solution:**

Given, Velocity of the bullet (v) = 0.1m/s

Mass of the bullet (m) = 25 g = 25/1000 kg = 0.025kg

Momentum (p) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

Therefore, `p = 0.025 kg xx 0.1 m//s`

Or, `p = 0.0025 kg m//s`

Thus the momentum of the bullet = 0.0025 kg m/s

Question 4: The mass of a goods lorry is 4000 kg and the mass of goods loaded on it is 20000 kg. If the lorry is moving with a velocity of 2m/s what will be its momentum?

**Solution:**

Given, Velocity (v) = 2m/s

Mass of lorry = 4000 kg, Mass of goods on the lorry = 20000 kg

Therefore, total mass (m) of the lorry = 4000 kg + 20000 kg = 24000 kg

Momentum (p) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

Therefore, `p = 24000 kg xx 2 m//s = 48000 kg m//s`

Thus, momentum of the lorry `= 48000 kg m//s`

Question 5: A car having mass of 1000 kg is moving with a velocity of 0.5m/s. What will be its momentum?

**Solution:**

Given, Velocity of the bullet (v) = 0.5m/s

Mass of the bullet (m) = 1000 kg

Momentum (p) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

Therefore, `p = 1000 kg xx 0.5 m//s`

Or, `p = 500 kg m//s`

Thus the momentum of the bullet `= 500 kg m//s`

**Type II: (Calculation of Mass)**

Question 1: A vehicle is running with a velocity of 5m/s. If the momentum of the vehicle is 5000 kg m/s, what is its mass?

**Solution:**

Given, Momentum (p) = 5000 kg m/s

Velocity (v) = 5m/s

Mass (m) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

Therefore, `5000 kg m//s = m xx 5m//s`

`=>m=(5000\ kg\ m//s)/(5m//s)=1000\ kg`

Thus, mass of the vehicle = 1000 kg

Question 2: A stone attains a momentum of 1 kg m/s when it flies with a velocity of 2m/s, then what will be mass of the stone?

**Solution:**

Given, Momentum (p) = 1 kg m/s

Velocity (v) = 2m/s

Mass (m) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

Therefore, `1 kg m//s = m xx 2m/s`

`=>m=(1\ kg\ m//s)/(2m//s)=0.5\ kg=500\ g`

Thus, mass of the stone = 0.5 kg or 500 g

Question 3: When a bullet is fired from a rifle its momentum become 20 kg m/s. If the velocity of the bullet is 1000m/s what will be its mass?

**Solution:**

Given, Momentum (p) = 20 kg m/s

Velocity (v) = 1000m/s

Mass (m) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

Therefore, `20 kg m//s = m xx 1000m//s`

`=>m=(20\ kg\ m//s)/(1000m//s)=1/50\ kg` `=0.02\ kg =20\ g`

Thus, mass of the bullet = 20 g

Question 4: When a missile is fired from a tank it gets a momentum of 2000 kg m/s. If the velocity of the missile is 50m/s what will be its mass?

**Solution:**

Given, Momentum (p) = 2000 kg m/s

Velocity (v) = 50m/s

Mass (m) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

Therefore, `2000 kg m//s = m xx 50 m//s`

`=>m=(2000\ kg\ m//s)/(50m//s)=40\ kg`

Thus, mass of the missile = 40 kg

Question 5: A bird is flying with a velocity of 3 m/s. If the momentum of the bird is 3.60 kg m/s what is its mass?

**Solution:**

Given, Momentum (p) = 3.60 kg m/s

Velocity (v) = 3 m/s

Mass (m) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

Therefore, `3.60 kg m//s = m xx 3 m//s`

`=>m=(3.60\ kg\ m//s)/(3m//s)=1.2\ kg=1\ kg\ 200\ g`

Thus, mass of the bird = 1 kg 200 g

## Type III (Calculation of velocity)

Question 1: If the momentum of a flying brick is 50 kg m/s and its mass is 10 kg. Calculate its velocity?

**Solution:**

Given, Momentum (m) = 50kg m/s

Mass (m) = 10kg

Velocity (v) =?

We know that,

Momentum (p) = Mass (m) x Velocity (v)

⇒ 50 kg m/s = 10kg × v

`=>v=(50\ kg\ m//s)/(10\ kg)=5m//s`

Thus, velocity of the brick = 5m/s

Question 2: A bullet of 25 g is when fired from a piston gets a momentum of 50 kg m/s. Calculate the velocity of bullet.

**Solution:**

Given, Momentum (m) = 50kg m/s

Mass (m) = 25 g = 25/1000 kg = 0.025 kg

Velocity (v) =?

We know that,

Momentum (p) = Mass (m) x Velocity (v)

⇒ 50 kg m/s = 0.025 kg × v

`=>v=(50\ kg\ m//s)/(0.025\ kg)=2000\ m//s`

Thus, velocity of the bullet = 2000 m/s

Question 3: A vulture when flying with a velocity ‘v’ attains a momentum of 20 kg m/s. If the mass of the vulture is 25 kg what is the value of ‘v’?

**Solution:**

Given, Momentum (m) = 20 kg m/s

Mass (m) = 25 kg

Velocity (v) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

⇒ 20 kg m/s = 25 kg × v

`=>v= (20\ kg\ m//s)/(25\ kg)=0.8\ m//s`

Thus, velocity of the vulture = 0.8 m/s

Question 4: A brick after falling from a hill collide with ground with a momentum of 100 kg m/s. If the mass of the brick is 5 kg what was its velocity while colliding with the ground?

**Solution:**

Given, Momentum (m) = 100kg m/s

Mass (m) = 5kg

Velocity (v) =?

We know that,

Momentum (p) = Mass (m) x Velocity (v)

⇒ 100 kg m/s = 5kg × v

`=>v=(100\ kg\ m//s)/(5\ kg)= 20\ m//s`

Thus, velocity of the brick = 20 m/s

Question 5: Calculate the velocity of a missile having mass of 100 kg, if it attains a momentum of 5000 kg m/s when fired from a rocket gun?

**Solution:**

Given, Momentum (m) = 5000kg m/s

Mass (m) = 100kg

Velocity (v) =?

We know that, Momentum (p) = Mass (m) x Velocity (v)

⇒ 5000 kg m/s = 100kg × v

`=>v= (5000\ kg\ m//s)/(100\ kg)= 50\ m//s`

Thus, velocity of the missile = 50 m/s