A block of mass m is suspended from a fixed support with the help of a cord. Another identical cord is attached to the bottom of the block. Which of the following statement is/are true?

Options

A. If the lower cord is pulled suddenly, only the upper cord will break.
B. If the lower cord is pulled suddenly, only the lower cord will break.
C. If pull on the lower cord is inceased gradually, only the upper cord will break.
D. If pull on the lower cord is increased gradually, only the lower cord will break.

Answer

To solve the problem, we need to analyze the situation of the block suspended by two cords and determine the truth of the given statements based on the physics of forces and tension in the cords.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a block of mass \( m \) suspended from a fixed support by an upper cord (let's call it cord C).
- Another identical cord (let's call it cord D) is attached to the bottom of the block.

2. **Analyzing the First Statement**:
- The first statement claims that if the lower cord (D) is pulled suddenly, only the upper cord (C) will break.
- When cord D is pulled suddenly, it experiences a sudden force (impulse). This impulse will not be transmitted instantaneously to cord C due to the inertia of the block.
- Therefore, the lower cord (D) is likely to break first, not the upper cord (C).
- **Conclusion**: This statement is **false**.

3. **Analyzing the Second Statement**:
- The second statement claims that if the lower cord (D) is pulled suddenly, only the lower cord (D) will break.
- As discussed, when cord D is pulled suddenly, it will experience a high tension due to the sudden force, and since it is the one being directly pulled, it is most likely to break first.
- **Conclusion**: This statement is **true**.

4. **Analyzing the Third Statement**:
- The third statement claims that if the pull on the lower cord (D) is increased gradually, the upper cord (C) will break.
- When the force is applied gradually, the tension in cord D will increase gradually, allowing the tension to be transmitted to cord C.
- Eventually, if the force exceeds the breaking strength of cord C, it will break.
- **Conclusion**: This statement is **true**.

5. **Analyzing the Fourth Statement**:
- The fourth statement claims that if the pull on the lower cord (D) is increased gradually, only the lower cord (D) will break.
- Since the force is applied gradually, the tension will increase in both cords, and if the force does not exceed the breaking point of cord D before reaching the breaking point of cord C, then cord D will not break first.
- Therefore, this statement is **false**.

### Final Summary of Statements:
- **Statement 1**: False
- **Statement 2**: True
- **Statement 3**: True
- **Statement 4**: False