All questions of Momentum for Grade 10 Exam

Given:
Mass of ball 1 (m1) = 5 kg
Velocity of ball 1 (u1) = 3 m/s
Mass of ball 2 (m2) = 3 kg
Velocity of ball 2 (u2) = 5 m/s
After the collision, the balls move together in the same direction.

To find: Common velocity of the balls after the collision.

Solution:

1. First, we need to find the momentum of each ball before the collision using the formula:

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

Momentum of ball 1 before the collision (p1) = m1u1 = 5 kg x 3 m/s = 15 kg m/s
Momentum of ball 2 before the collision (p2) = m2u2 = 3 kg x 5 m/s = 15 kg m/s

2. Next, we need to find the total momentum of the system before the collision (p):

Total momentum before the collision (p) = p1 + p2 = 15 kg m/s + 15 kg m/s = 30 kg m/s

3. During the collision, the balls stick together and move with a common velocity (v). Using the law of conservation of momentum, we can equate the total momentum before the collision (p) to the total momentum after the collision (p'):

Total momentum after the collision (p') = (m1 + m2) x v

4. Equating the two expressions for total momentum, we get:

p = p'
30 kg m/s = (5 kg + 3 kg) x v

5. Solving for v, we get:

v = 30 kg m/s ÷ 8 kg = 3.75 m/s

Therefore, the common velocity of the balls after the collision is 3.75 m/s.

Answer: Option B (3.75 m/s)

The correct answer is option B: the momentum of a body is proportional to its velocity.

Explanation:

1. Understanding momentum:
- Momentum is a property of a moving object that describes its motion.
- It is defined as the product of an object's mass and its velocity.
- Mathematically, momentum (p) is given by the equation p = m * v, where m is the mass of the object and v is its velocity.

2. Proportional relationship:
- When two quantities are said to be proportional to each other, it means that they vary in direct proportion.
- In this case, the momentum is proportional to the velocity, which means that as the velocity increases, the momentum also increases, and vice versa.
- This relationship can be expressed as p ∝ v.

3. Understanding mass and volume:
- Mass refers to the amount of matter contained in an object, and it remains constant regardless of the object's location or state of motion.
- Volume, on the other hand, refers to the amount of space occupied by an object.
- While both mass and volume are important properties of matter, they do not directly affect the momentum of an object.

4. Color and shape:
- The color of an object and its shape do not have any influence on its momentum.
- These characteristics are related to the object's physical appearance and do not affect its motion or the forces acting upon it.

5. Velocity and momentum:
- Velocity is a measure of how fast an object is moving in a particular direction.
- The greater the velocity of an object, the greater its momentum.
- This relationship can be understood intuitively by considering a moving car: a car traveling at a higher velocity will have more momentum and will be harder to stop compared to a car traveling at a lower velocity.

In conclusion, the momentum of a body is proportional to its velocity. This means that as the velocity of an object increases, its momentum also increases, and as the velocity decreases, the momentum decreases. The mass of the object remains constant in this relationship. The color, volume, and shape of an object do not have any influence on its momentum.

Conservation of momentum. A conservation law stating that the total linear momentum of a closed system remains constant through time, regardless of other possible changes within the system.

If there is no force acting on the system, then there will be no change in the moment of the system, Hence the total momentum will remain conserved