Example-01: What will be the momentum of a stone having mass of 10 kg when it is thrown with a velocity of 2 m/s?
Solution: Given, Mass (m) = 10 kg
Velocity (v) = 2 m/s
Momentum (p) = ?
We know that, Momentum (p) = Mass (m) x Velocity (v)
Therefore, p=10 kg × 2 m/s = 20 kgm/s
Thus the momentum of the stone = 20 kgm/s
Example-02: Calculate the momentum of a bullet of 25 g when it is fired from a gum with a velocity of 100 m/s.
Solution: Given, Velocity of the bullet (v) = 100 m/s
Mass of the bullet (m) = 25 g = 25/1000 kg = 0.025 kg
Momentum (p) = ?
or, p = 2.5 kgm/s
Thus the momentum of the bullet = 2.5 kgm/s
Example-03: 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 = 0.025 kg
Momentum (p) = ?
We know that, Momentum (p) = Mass (m) x Velocity (v)
Therefore, p=0.025 kg × 0.1m/s
or, p=0.0025 kgm/s. Thus the momentum of the bullet = 0.0025 kg m/s
Example-04: 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 2 m/s what will be its momentum ?
Solution: Given, Velocity (v) = 2 m/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×2 m/s = 48000 kgm/s
Thus, momentum of the lorry = 48000 kgm/s
Example-05: A car having mass of 1000 kg is moving with a velocity of 0.5 m/s. What will be its momentum?
Solution: Given, Velocity of the bullet (v) = 0.5 m/s
Mass of the bullet (m) = 1000 kg
Momentum (p) = ?
We know that, Momentum (p) = Mass (m) x Velocity (v)
Therefore, p = 1000 kg × 0.5 m/s
or, p = 500 kgm/s. Thus the momentum of the bullet = 500 kgm/s
Example-06: A vehicle is running with a velocity of 5 m/s. If the momentum of the vehicle is 5000 kgm/s, what is its mass?
Solution: Given, Momentum (p) = 5000 kgm/s
Velocity (v) = 5 m/s
Mass (m) = ?
We know that, Momentum (p) = Mass (m) x Velocity (v)
Therefore, 5000 kgm/s = m × 5 m/s
⇒ m = 5000 kgms^{-1} / 5 ms^{-1} = 1000 kg
Thus, mass of the vehicle = 1000 kg
Example-07: A stone attains a momentum of 1 kg m/s when it flies with a velocity of 2 m/s, then what will be mass of the stone?
Solution: Given, Momentum (p) = 1 kg m/s
Velocity (v) = 2 m/s
Mass (m) = ?
We know that, Momentum (p) = Mass (m) x Velocity (v)
Therefore, 1 kgm/s = m × 2 m/s
⇒ m = 1 kgms^{-1}/ 2 ms^{-1} = 0.5 kg = 500 g
Thus, mass of the stone = 0.5 kg or 500 g
Example-08: When a bullet is fired from a rifle its momentum become 20 kgm/s. If the velocity of the bullet is 1000 m/s what will be its mass?
Solution: Given, Momentum (p) = 20 kgm/s
Velocity (v) = 1000 m/s
Mass (m) = ?
We know that, Momentum (p) = Mass (m) x Velocity (v)
Therefore, 20 kgm/s = m × 1000 m/s
⇒ m = 20 kgms^{-1} /1000 ms^{-1} = 150 kg = 0.02 kg = 20 g
Thus, mass of the bullet = 20 g
Example-09: When a missile is fired from a tank it gets a momentum of 2000 kg m/s. If the velocity of the missile is 50 m/s what will be its mass?
Solution: Given, Momentum (p) = 2000 kgm/s
Velocity (v) = 50 m/s
Mass (m) = ?
We know that, Momentum (p) = Mass (m) x Velocity (v)
Therefore, 2000 kgms^{-1} = m × 50 ms^{-1}
⇒ m = 2000 kgms^{-1} /50 ms^{-1} = 40 kg
Thus, mass of the missile = 40 kg
Example-10: A bird is flying with a velocity of 3 m/s. If the momentum of the bird is 3.60 kgm/s what is its mass ?
Solution: Given, Momentum (p) = 3.60 kgm/s
Velocity (v) = 3 m/s
Mass (m) = ?
We know that, Momentum (p) = Mass (m) x Velocity (v)
Therefore, 3.60 kgm/s = m × 3 ms^{-1}
⇒ m = 3.60 kg ms^{-1}/ 3 ms^{-1} = 1.2 kg =1 kg 200 g
Thus, mass of the bird = 1 kg 200 g
Example-11: If the momentum of a flying brick is 50 kgm/s and its mass is 10 kg. Calculate its velocity?
Solution: Given, Momentum (m) = 50 kgm/s
Mass (m) = 10 kg
Velocity (v) = ?
We know that,
Momentum (p) = Mass (m) x Velocity (v)
⇒ 50 kg m/s = 10kg × v
⇒ v = 50 kgms^{-1}/10 kg= 5 ms^{-1}
Thus, velocity of the brick = 5 ms^{-1}
Example-12: A bullet of 25 g is when fired from a piston gets a momentum of 50 kgm/s. Calculate the velocity of bullet.
Solution:
Given, Momentum (m) = 50 kgm/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 kgms^{-1}/0.025 kg = 2000 ms^{-1}
Thus, velocity of the bullet = 2000 ms^{-1}
Example-13: 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 kgm/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 kgms^{-1} /25 kg = 0.8 ms^{-1}
Thus, velocity of the vulture = 8 ms^{-1}
Example-14: A brick after falling from a hill collide with ground with a momentum of 100 kgm/s. If the mass of the brick is 5 kg what was its velocity while colliding with the ground?
Solution:
Given, Momentum (m) = 100 kgm/s
Mass (m) = 5 kg
Velocity (v) = ?
We know that,
Momentum (p) = Mass (m) x Velocity (v)
⇒ 100 kgm/s = 5 kg × v
⇒ v = 100 kgms^{-1} /5 kg = 20 m/s
Thus, velocity of the brick = 20 m/s
Example-15: Calculate the velocity of a missile having mass of 100 kg, if it attains a momentum of 5000 kgm/s when fired from a rocket gun?
Solution:
Given, Momentum (m) = 5000 kgm/s
Mass (m) = 100 kg
Velocity (v) = ?
We know that, Momentum (p) = Mass (m) x Velocity (v)
⇒ 5000 kg m/s = 100 kg × v
⇒ v = 5000 kg ms^{-1} /100 kg = 50 m/s
Thus, velocity of the missile = 50 m/s