Class 9 Forces and Laws of Motion Numerical Problems Based on Momentum

Forces and Laws of Motion

Momentum

Numerical Problems Based on Momentum

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) x Velocity (v)
Therefore, p = 10kg x 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 x 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 x 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 x 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 × 5m/s

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 × 2m/s

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 × 1000m/s

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 × 50 m/s

Thus, mass of the missile = 40 g

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 × 3 m/s

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

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

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

Thus, velocity of the vulture = 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

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

Thus, velocity of the missile = 50 m/s