Conservation of Linear Momentum Important Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Two external forces are acting on a system of particles. Select the correct statement.

1. Linear momentum may be conserved
2. The center of mass will move with increasing speed
3. Linear momentum is necessarily not conserved
4. Linear momentum is zero

Ans. The correct answer is a. Linear momentum may be conserved

Explanation: The conservation of linear momentum depends on the net force acting on the body. If the net force is zero, then linear momentum is conserved.

Ques. What is the unit of linear momentum?

1. kg s^-1
2. kg m s^-2
3. kg m s^-1
4. kg m^-1

Ans. The correct answer is c. kg m s^-1

Explanation: The SI unit of linear momentum is kg m s^-1

Ques. For a body moving with relativistic speed, if the velocity is doubled then

1. Its linear momentum is doubled
2. Its linear momentum will be less than double
3. Its linear momentum will be more than double
4. Its linear momentum remains unchanged

Ans. The correct answer is c. Its linear momentum will be more than double

Explanation: Relativistic momentum is given by

\(p = \frac{m_0v}{\sqrt{1- \frac{v^2}{c^2}}}\)

If the velocity is doubled then the relativistic mass also increases. Thus the value of the linear momentum will be more than double.

Ques. Newton’s second and third laws of motion lead to the conservation of

1. Linear momentum
2. Angular momentum
3. Potential energy
4. Kinetic energy

Ans. The correct answer is a. Linear momentum

Explanation: Newton’s second and third laws of motion lead to the conservation of linear momentum.

Ques. A body, whose momentum is constant, must have constant

1. Acceleration
2. Force
3. Velocity
4. All of the above

Ans. The correct answer is c. Velocity

Explanation: For a given mass, the momentum of a body is directly proportional to its velocity. Hence if the momentum of a body is constant, then the body must have constant velocity.

Ques. The motion of a rocket is based on the principle of conservation of

1. Kinetic energy
2. Mass
3. Angular momentum
4. Linear momentum

Ans. The correct answer is d. Linear momentum

Explanation: Rocket propulsion is based on the concept of linear momentum conservation since the rocket is initially at rest, but when ready to lift off, the momentum of the small amount of gas ejected at high speed is balanced by increasing the momentum of the rocket with the remaining fuel.

Ques. Linear momentum is a

1. Vector quantity
2. Scalar quantity
3. Dimensionless quantity
4. None of the above

Ans. The correct answer is a. Vector quantity

Explanation: Linear momentum is a vector quantity and its direction is the same as that of the direction of velocity.

Ques. According to Newton’s second law, force is directly proportional to the rate of change in

1. Velocity
2. Momentum
3. Acceleration
4. Mass

Ans. The correct answer is b. Momentum

Explanation: Newton's second law states that the rate of change of the momentum of the body is equal to the force applied to it in both magnitude and direction.

Ques. The linear momentum of a particle is the product of ______ of that particle.

1. The mass of the particle times the acceleration
2. The mass of the particle times the velocity
3. The mass of the particle times the kinetic energy
4. The mass of the particle times the momentum

Ans. The correct answer is b. The mass of the particle times the velocity

Explanation: The linear momentum of a particle is the product of the mass of the particle times the velocity of that particle.

Ques. In a falling body with a constant amount of energy, potential energy changes to

1. Nuclear energy
2. Thermal energy
3. Kinetic energy
4. Solar energy

Ans. The correct answer is c. Kinetic energy

Explanation: In a falling body with a constant amount of energy, potential energy changes to kinetic energy, but the total mechanical energy remains constant.

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Short Answers Questions [2 Marks Questions]

Ques. What is the conservation of linear momentum?

Ans. The conservation of linear momentum is an essential law of physics that says that unless an external force acts on a system of objects, the total linear momentum of the system remains constant.

Ques. Define linear momentum.

Ans. Linear momentum, also known as the momentum of the body, is defined as the total amount of motion contained by a moving body and can be measured as the product of the mass and velocity of the particle. Momentum is a vector quantity.

Ques. What is the formula of linear momentum?

Ans. Let a body of mass m move with velocity v then the linear momentum of the body is given by

p = m x v

Where

• p is the linear momentum of the body
• m is the mass of the body
• v is the velocity of the body

Ques. Determine the linear momentum of a boy with a mass of 10 kg and moving with a velocity of 80 m/s.

Ans. Given

• Mass of the boy, m = 10 kg
• The velocity of the boy, v = 80 m/s

Linear momentum of the body, p = mv

⇒ p = 10 x 80 = 800 kg m/s

Ques. What is the formula for the conservation of linear momentum?

Ans. Let two bodies of masses m₁ and m₂ move with velocities v₁ and v₂ collide with each other. After the collision the velocities of both bodies become v₁ and v₂, then according to the law of conservation of linear momentum, we have

Initial momentum = Final momentum

⇒ m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Ques. What if momentum is not conserved?

Ans. Momentum is not conserved when gravity, friction, or net force are present; net force refers to the overall amount of force. It demonstrates that if these quantities act on any object, its momentum will change. This should be noticeable because you are changing the object's velocity and momentum.

Ques. What is recoil velocity?

Ans. When a bullet is fired from the gun, the gun experiences a backward force. The gun acquires velocity in the opposite direction as a result of this force. This is referred to as recoil velocity.

Ques. Is the total momentum of the universe constant?

Ans. The total momentum of the universe remains constant. There is no system bigger than the universe itself. As there is no outside force acting on the universe, its linear momentum is conserved.

Ques. Determine the linear momentum of a body with a mass of 5 kg and moving with a velocity of 50 m/s.

Ans. Given

• Mass of the body, m = 5 kg
• The velocity of the body, v = 50 m/s

Linear momentum of the body, p = mv

⇒ p = 5 x 50 = 250 kg m/s

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Long Answers Questions [3 Marks Questions]

Ques. What are the applications of the law of conservation of linear momentum?

Ans. Linear momentum is important in rocket propulsion as well as the recoil of a gun. They are as follows:

• Rocket propulsion: Chemicals in the rocket ignite and rapidly release gases. These gases exit the tail nozzle in a downward direction, causing the rocket to rise in order to balance the momentum of the gases. Even if the volume of gas ejected is small, the velocity adds up to momentum. Despite its large mass, the rocket goes upward at a high velocity because it gets equivalent momentum in the opposite direction.
• The recoil of a gun: When a bullet is fired from a gun, to balance the momentum imparted by the bullet, the gun moves backward with a recoil velocity. Recoil velocity is the speed with which a gun goes backward after firing a bullet.
• Motion of the motorboats: Motorboats work on the same principle, pushing the water back and forth to conserve momentum.

Ques. Give the applications of Newton’s second law.

Ans. Newton's second law of motion may be used to calculate the amount of force required to move or stop an object.

Some applications of Newton’s second law of motion are

• Kicking a ball: When we kick a ball, we only exert force in one direction. The greater the force we put on the ball when we kick it, the farther it will travel.
• Pushing a cart: An empty cart is easier to push than a full cart in a supermarket because more mass requires more acceleration.
• Two people walking: If one of the two people walking is heavier than the other, the larger person will walk slower since the lighter person's acceleration is higher.

Ques. A boy with a 50 kg mass is running with a velocity of 2 m/s. He jumps over a stationary cart of 2 kg while running. Find the velocity of the cart after the jumping of the boy.

Ans. Given

• The mass of the boy, m₁ = 50 kg
• Initial Velocity of the boy, u₁ = 2 m/s
• Mass of the cart, m₂ = 2 kg
• The initial velocity of the cart, u₂ = 0

Let v₁ and v₂ be the final velocities of the boy and cart respectively.

Because the boy jumped over the cart, his final velocity (v₁) will be equal to that of the cart i.e.

v₁ = v₂ = v

According to the law of conservation of linear momentum

(m₁u₁ + m₂u₂) = (m₁v₁ + m₂v₂)

Since v₁ = v₂ = v, therefore

⇒ (m₁u₁ + m₂u₂) = (m₁v + m₂v)

⇒ (m₁u₁ + m₂u₂) = (m₁+ m₂)v

⇒ v = (m₁u₁ + m₂u₂)/(m₁+ m₂)

⇒ v = (50 x 2 + 2 x 0)/(50 + 2)

⇒ v = 100/52 = 1.92 m/s

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Very Long Answers Questions [5 Marks Questions]

Ques. Two objects each of mass 5 kg are moving in the same straight line but in opposite directions toward each other with the same speed of 3 m/s. They are stuck to each other after the collision. What will be the velocity of the combined object after collision?

Ans. Let m₁ and m₂ be the masses of the two objects moving with velocities u1 and u2 in opposite directions.

Given

• m₁ = m₂ = 5 kg
• The velocity of the first object, u₁ = 3 m/s
• The velocity of the second object, u₂ = – 3 m/s

Total momentum before the collision is given by

p_i = m₁u₁ + m₂u₂

⇒ p_i = (5 x 3) + (5 x -3) = 0

After the collision, both bodies stick together and move with velocity v.

Therefore, total momentum after collision, p_f = (m₁ + m₂)v

⇒ p_f = (5 + 5)v = 10v

According to the law of conservation of momentum, p_f = p_i

⇒ 10v = 0

⇒ v = 0

Hence the velocity of the combined object is zero.

Ques. Derive the law of conservation of linear momentum from Newton’s third law of motion.

Ans. Consider two bodies A and B of masses m1 and m2 in an isolated system, initially moving with velocities u₁ and u₂ respectively, therefore

The total momentum before the collision

p_i = m₁u₁ + m₂u₂

Let the bodies move with velocities v₁ and v₂ after collision, then

The total momentum after collision

p_f = m₁v₁ + m₁v₂

Change in the momentum of body A after collision is given by

Δp_A = m₁v₁ – m_1u1

Change in the momentum of body B after collision is given by

Δp_B = m₂v₂ – m₂u₂

During collision body A and B exerts force on each other in opposite direction. Thus from Newton’s third law of motion

Force on B due to A, F_BA = - (Force on A due to B, FAB)

The impulse of force acting on body A = Change in momentum of body A

⇒ F_ABΔt = m₁v₁ - m₁u₁

The impulse of force acting on body B = Change in the momentum of body B

⇒ F_BAΔt = m₂v₂ - m₂u₂

Since F_BA = –  F_AB, therefore

(m₂v₂ - m₂u₂) = - (m₁v₁ - m₁u₁)

⇒ (m₁u₁ + m₂u₂) = (m₁v₁ + m₂v₂)

The above equation shows that the change in momentum before collision equals the change in momentum after collision.

Ques. A bullet of mass 40 g is fired from a gun with an initial velocity of 25 m/s. If the mass of the gun is 3 kg, then calculate the recoil velocity of the gun.

Ans. Recoil velocity is the speed with which a gun goes backward after firing a bullet.

Let

• v₁ be the velocity of the bullet after firing
• v₂ be the recoil velocity of the gun i.e. velocity of the gun after firing
• m₁ be the mass of the bullet
• m₂ be the mass of the gun
• u₁ and u₂ are the velocities of the bullet and the gun before firing

Given

• m₁ = 40 g = 40 x 10^-3 kg
• m₂ = 3 kg
• v₁ = 25 m/s

Before firing, u₁ = u₂ = 0

Total linear momentum before firing,

P_i = m₁u₁ + m₂u₂

⇒ P_i = (40 x 10^-3 x 0) + (3 x 0)

⇒ P_i = 0

Total linear momentum after firing,

P_f = m₁v₁ + m₂v₂

⇒ P_f = (40 x 10_-3 x 25) + (3 x v₂)

⇒ P_f = 1 + 3v₂

According to the conservation of linear momentum, total momentum before collision is equal to the total momentum after collision i.e.

P_i = P_f

⇒ 0 = 1 + 3v₂

⇒ v₂ = - 1/3

⇒ v₂ = - 0.33 m/s

Hence the recoil velocity of the gun is 0.33 m/s. The negative sign indicates that the recoil velocity is pointing in the opposite direction as the bullet.

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