When a bullet is fired from a gun

Options

A. (a) The kinetic energy of the bullet is more than that of the gum
B. (b) The acceleration of the bullet is more than that of the gun
C. (c) The momentum of the bullet is more than that of the gun
D. (d) The velocity of the bullet is more than that of the gun

Explanation

To solve the question regarding the bullet being fired from a gun, we will analyze the statements provided and determine their validity based on the principles of physics, particularly focusing on kinetic energy, momentum, and acceleration.

### Step-by-Step Solution:

1. **Understanding Kinetic Energy**:
- The kinetic energy (KE) of an object is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
- When a bullet is fired, it has a high velocity compared to the gun, which has a much larger mass but a lower velocity due to recoil.

2. **Comparing Kinetic Energies**:
- Let's denote:
- Mass of the bullet \( m_b = 20 \, \text{grams} = 0.02 \, \text{kg} \)
- Velocity of the bullet \( v_b = 400 \, \text{m/s} \)
- Mass of the gun \( m_g = 400 \, \text{grams} = 0.4 \, \text{kg} \)
- Velocity of the gun (recoil) \( v_g \) is much less, say \( 1 \, \text{m/s} \).
- Calculate the kinetic energies:
- For the bullet:
\[ KE_b = \frac{1}{2} m_b v_b^2 = \frac{1}{2} \times 0.02 \times (400)^2 = 1600 \, \text{J} \]
- For the gun:
\[ KE_g = \frac{1}{2} m_g v_g^2 = \frac{1}{2} \times 0.4 \times (1)^2 = 0.2 \, \text{J} \]
- Conclusion: The kinetic energy of the bullet is much greater than that of the gun.

3. **Comparing Accelerations**:
- The acceleration of an object can be defined as the change in velocity over time. Since the bullet accelerates rapidly to a high speed while the gun recoils slowly, it can be concluded that:
- The acceleration of the bullet is greater than that of the gun.

4. **Comparing Momentum**:
- Momentum (P) is given by:
\[ P = mv \]
- Calculate the momenta:
- For the bullet:
\[ P_b = m_b v_b = 0.02 \times 400 = 8 \, \text{kg m/s} \]
- For the gun:
\[ P_g = m_g v_g = 0.4 \times 1 = 0.4 \, \text{kg m/s} \]
- Conclusion: The momentum of the bullet is greater than that of the gun.

5. **Comparing Velocities**:
- The bullet exits the gun at a high speed (400 m/s) while the gun has a very low recoil velocity (1 m/s).
- Conclusion: The velocity of the bullet is indeed greater than that of the gun.

### Final Answers:
- **Option A**: The kinetic energy of the bullet is more than that of the gun. **(True)**
- **Option B**: The acceleration of the bullet is more than that of the gun. **(True)**
- **Option C**: The momentum of the bullet is more than that of the gun. **(True)**
- **Option D**: The velocity of the bullet is more than that of the gun. **(True)**

Thus, the correct options are A, B, C, and D.