Answer :
To understand the relationships between momentum (p), mass (m), and velocity (v), let's analyze each formula given:
1. \( p = m v \)
- This is the fundamental formula for momentum. Momentum is defined as the product of mass and velocity.
- This formula is correct.
2. \( p = \frac{m}{v} \)
- This formula suggests that momentum is equal to the mass divided by the velocity.
- This does not align with the fundamental definition of momentum.
- This formula is incorrect.
3. \( p = \frac{v}{m} \)
- This formula suggests that momentum is equal to the velocity divided by the mass.
- This also does not correspond to the basic definition of momentum.
- This formula is incorrect.
4. \( m = \frac{p}{v} \)
- This can be derived from the fundamental formula \( p = m v \).
- Rearranging for \( m \) gives \( m = \frac{p}{v} \).
- This formula is correct.
5. \( p = \frac{v}{p} \)
- This implies that momentum is equal to velocity divided by momentum, which is nonsensical in the context of units and the definition of momentum.
- This formula is incorrect.
6. \( v = \frac{p}{m} \)
- This can also be derived from \( p = m v \).
- Rearranging for \( v \) gives \( v = \frac{p}{m} \).
- This formula is correct.
7. \( v = \frac{m}{p} \)
- This formula suggests that velocity is equal to mass divided by momentum, which is not consistent with the fundamental relationship of momentum.
- This formula is incorrect.
So, the formulas that show the correct relationships between momentum, mass, and velocity are:
1. \( p = m v \)
2. \( m = \frac{p}{v} \)
3. \( v = \frac{p}{m} \)
These three formulas correctly express the relationships between the variables based on the fundamental definition of momentum.
1. \( p = m v \)
- This is the fundamental formula for momentum. Momentum is defined as the product of mass and velocity.
- This formula is correct.
2. \( p = \frac{m}{v} \)
- This formula suggests that momentum is equal to the mass divided by the velocity.
- This does not align with the fundamental definition of momentum.
- This formula is incorrect.
3. \( p = \frac{v}{m} \)
- This formula suggests that momentum is equal to the velocity divided by the mass.
- This also does not correspond to the basic definition of momentum.
- This formula is incorrect.
4. \( m = \frac{p}{v} \)
- This can be derived from the fundamental formula \( p = m v \).
- Rearranging for \( m \) gives \( m = \frac{p}{v} \).
- This formula is correct.
5. \( p = \frac{v}{p} \)
- This implies that momentum is equal to velocity divided by momentum, which is nonsensical in the context of units and the definition of momentum.
- This formula is incorrect.
6. \( v = \frac{p}{m} \)
- This can also be derived from \( p = m v \).
- Rearranging for \( v \) gives \( v = \frac{p}{m} \).
- This formula is correct.
7. \( v = \frac{m}{p} \)
- This formula suggests that velocity is equal to mass divided by momentum, which is not consistent with the fundamental relationship of momentum.
- This formula is incorrect.
So, the formulas that show the correct relationships between momentum, mass, and velocity are:
1. \( p = m v \)
2. \( m = \frac{p}{v} \)
3. \( v = \frac{p}{m} \)
These three formulas correctly express the relationships between the variables based on the fundamental definition of momentum.
