Forces and Laws of Motion

Momentum

Numertical 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 

    m   =       5000 kg m/s       =  1000 kg

                      5 m/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

m = 1kg m/s  = 0.5 kg = 500 gm

          2 m/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

    m = 20 kg m/s  =  1  kg  = 0.02 Kg = 20 gm

           1000 m/s      50

   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

      m = 2000 kg m/s  = 40 kg

               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

  m = 3.60 kg m/s =  1.20 kg = 1 kg 200gm

          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

   v = 50 kg m/s  = 5 m/s

          10 kg     

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  = 2000 m/s

           0.025 kg

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  =0.8 m/s

           25 kg    

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

    v = 100 kg m/s  = 20 m/s

           5 kg

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  = 50 m/s

             100 kg    

Thus, velocity of the missile = 50 m/s

NCERT In Text Solution

Question:- 1 - Which of the following has more inertia:

(a) a rubber ball and a stone of the same size?

(b) a bicycle and a train?

(c) a five rupees coin and a one-rupee coin?

Answer:-

(a) A stone.

(b) A train

(c) A five rupees coin.

Explanation – Inertia is associated with mass. Objects having more mass have more inertia.

Question:- 2 - In the following example, try to identify the number of times the velocity of the ball changes:

“A football player kicks a football to another player of his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own team”. Also identify the agent supplying the force in each case.

Answer:

The velocity of football changes four times.

First, when a football player kicks to another player, second when that player kicks the football to the goalkeeper. Third when the goalkeeper stops the football. Fourth when the goalkeeper kicks the football towards a player of his own team.

Agent supplying the force –

First case – First player

Second case – Second player

Third case – Goalkeeper

Fourth case – Goalkeeper

Question: 3 - Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.

Answer: The answer of this cause lies behind the Newton’s First Law of Motion. Initially, leaves and tree both are in rest. But when the tree is shaken vigorously, tree comes in motion while leaves have tendency to be in rest. Thus, because of remaining in the position of rest some of the leaves may get detached from a tree if we vigorously shake its branch.

Question: 4 - Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?

Answer:

In a moving bus, passengers are in motion along with bus. When brakes are applied to stop a moving bus, bus comes in the position of rest. But because of tendency to be in the motion a person falls in forward direction.

Similarly, when a bus is accelerated from rest, the tendency to be in rest, a person in the bus falls backwards.

Question: 5 - If action is always equal to the reaction, explain how a horse can pull a cart.

Answer: Horse pushes the ground in backward direction. In reaction to this, the horse moves forward and cart moves along with horse in forward direction.

In this case when horse tries to pull the cart in forward direction, cart pulls the horse in backward direction, but because of the unbalanced force applied by the horse, it pulls the cart in forward direction.

Question: 6 - Explain, why is it difficult for a fireman to hold a hose, which ejects large amounts of water at a high velocity.

Answer: When large amount of water is ejected from a hose at a high velocity, according to Newton’s Third Law of Motion, water pushes the hose in backward direction with the same force. Therefore, it is difficult for a fireman to hold a hose in which ejects large amount of water at a high velocity.