Read the given paragraph and answer the following questions
Two metal rulers of lengths 30 cm and 60 cm are kept in such a manner that a 30 cm ruler extends about 15 cm over the edge of a table and a 60 cm ruler extends about 30 cm over the edge of same table. Both the free ends are flicked.
Which of the following statements are correct regarding this?
(i) The metal ruler of length 30 cm is able to vibrate slower.
(ii) The metal ruler of length 30 cm produces a high pitch sound
(iii) The metal ruler of length 60 cm is able to vibrate faster.
(iv) The metal ruler of length 60 cm produces a low pitch sound.

Options

A. Only (i) and (iii) are correct
B. Only (ii) and (iv) are correct.
C. Only (i) and (iv) are correct.
D. Only (ii) and (iii) are correct.

Explanation

To solve the question, we need to analyze the behavior of the two metal rulers when they are flicked. The key concepts involved are the relationship between the length of a vibrating object and the frequency of the sound it produces.

### Step-by-Step Solution:

1. **Understanding Vibrations and Frequency**:
- When a ruler is flicked, it vibrates and produces sound. The frequency of the sound produced is related to the length of the ruler. Generally, shorter objects vibrate faster and produce higher frequency sounds, while longer objects vibrate slower and produce lower frequency sounds.

2. **Analyzing the 30 cm Ruler**:
- The 30 cm ruler is shorter than the 60 cm ruler. Therefore, it will vibrate faster than the 60 cm ruler. This means that it will produce a higher frequency sound, which corresponds to a high pitch.

3. **Analyzing the 60 cm Ruler**:
- The 60 cm ruler is longer than the 30 cm ruler. As a result, it will vibrate slower than the 30 cm ruler. This slower vibration leads to a lower frequency sound, which corresponds to a low pitch.

4. **Evaluating the Statements**:
- (i) The metal ruler of length 30 cm is able to vibrate slower. **(Incorrect)**
- (ii) The metal ruler of length 30 cm produces a high pitch sound. **(Correct)**
- (iii) The metal ruler of length 60 cm is able to vibrate faster. **(Incorrect)**
- (iv) The metal ruler of length 60 cm produces a low pitch sound. **(Correct)**

5. **Conclusion**:
- The correct statements are (ii) and (iv). The 30 cm ruler produces a high pitch sound, and the 60 cm ruler produces a low pitch sound.

### Summary of Correct Statements:
- (ii) The metal ruler of length 30 cm produces a high pitch sound.
- (iv) The metal ruler of length 60 cm produces a low pitch sound.