Overview:
King Kharvela was a prominent ruler of Kalinga during the 2nd century BCE. He was associated with the Mahameghavahana dynasty, which ruled over Kalinga. The other options mentioned in the question, namely Chedi dynasty, Satavahana dynasty, and Rath-Bhojak dynasty, are not associated with King Kharvela.

Explanation:

1. Mahameghavahana dynasty:
- King Kharvela was a part of the Mahameghavahana dynasty, which ruled over Kalinga (present-day Odisha) during the 2nd century BCE.
- The Mahameghavahana dynasty is also known as the Chedi dynasty.
- King Kharvela is considered one of the most famous kings of this dynasty and is known for his military conquests and patronage of Buddhism.

2. Chedi dynasty:
- The Chedi dynasty and the Mahameghavahana dynasty are different names for the same ruling dynasty of Kalinga.
- King Kharvela was a prominent ruler of this dynasty and played a vital role in expanding its territories and influence.

3. Satavahana dynasty:
- The Satavahana dynasty was a South Indian dynasty that ruled over a significant part of the Deccan region during the same time period as King Kharvela.
- King Kharvela and the Mahameghavahana dynasty were not associated with the Satavahana dynasty.
- The Satavahana dynasty had its own rulers and territories separate from Kalinga.

4. Rath-Bhojak dynasty:
- The Rath-Bhojak dynasty is not associated with King Kharvela or the Mahameghavahana dynasty.
- The Rath-Bhojak dynasty was a ruling dynasty in Gujarat during the medieval period and is unrelated to the time and region in which King Kharvela ruled.

Conclusion:
From the above explanation, it is clear that King Kharvela was associated with the Mahameghavahana dynasty (also known as the Chedi dynasty) of Kalinga. The other options mentioned in the question, namely Chedi dynasty, Satavahana dynasty, and Rath-Bhojak dynasty, are not associated with King Kharvela.