M.S. Nagaraja is associated with the study of Hampi due to his significant contributions to the research and preservation of the historical and archaeological heritage of the ancient city of Hampi. Hampi is a UNESCO World Heritage Site located in the Indian state of Karnataka, and it was the capital of the Vijayanagara Empire. M.S. Nagaraja is known for his work in the field of history, art, and archaeology, particularly related to Hampi and the Vijayanagara Empire. His research and publications have played a crucial role in advancing our understanding of the history, culture, and architecture of this remarkable site. His work includes studies on the monuments, inscriptions, and other historical aspects of Hampi, making him a prominent authority in this field.

So, the correct option is [1].