Which of the following is/are true about the impulse ?

Options

A. A weak force acting for a longer duration and a strong force acting for a short duration can produce the same impulse.
B. Impulse has the same relation with momentum as work has with kinetic energy.
C. Impulse acting on a body always changes its kinetic energy.
D. None of above

Answer

To determine which statements about impulse are true, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Impulse**:
- Impulse (I) is defined as the product of force (F) and the time duration (dt) over which the force acts. Mathematically, it can be expressed as:
\[ I = F \cdot dt \]
- Impulse can also be understood as the change in momentum (Δp) of an object:
\[ I = \Delta p = p_f - p_i \]
where \( p_f \) is the final momentum and \( p_i \) is the initial momentum.

2. **Analyzing Option 1**:
- The statement claims that a weak force acting for a longer duration can produce the same impulse as a strong force acting for a shorter duration.
- This is true because if \( F_1 \cdot dt_1 = F_2 \cdot dt_2 \), then both can yield the same impulse. Hence, this option is correct.

3. **Analyzing Option 2**:
- The statement suggests that impulse has the same relation with momentum as work has with kinetic energy.
- This is also true. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. Similarly, impulse is equal to the change in momentum:
\[ W = \Delta KE \quad \text{and} \quad I = \Delta p \]
- Therefore, this option is correct as well.

4. **Analyzing Option 3**:
- The statement claims that impulse acting on a body always changes its kinetic energy.
- This is false. Impulse can change the momentum of an object without necessarily changing its kinetic energy. For example, if a body is acted upon by an impulse that reverses its direction but maintains the same speed, the kinetic energy remains unchanged while the momentum changes.
- Therefore, this option is incorrect.

### Conclusion:
- The correct statements about impulse are:
- **Option 1**: True
- **Option 2**: True
- **Option 3**: False

### Final Answer:
Options 1 and 2 are true about impulse.

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