When dealing with questions about authors of specific historical, philosophical, or social works, especially concerning Indian history and social reform, it's often helpful to associate prominent figures with their key contributions and literary works. Dr. (B)R. Ambedkar's extensive writings on the caste system and his efforts for social justice make him a significant figure in this context.
Step 1: Identify the book in question.
The question asks to identify the author of the book titled "Who were the Shudras?".
Step 2: Recall the prominent works of the listed authors related to Indian history and social issues. Mahatma Gandhi: A key leader of the Indian independence movement, known for his philosophy of nonviolent resistance. His famous works include 'Hind Swaraj' and 'The Story of My Experiments with Truth'. While he extensively wrote on social issues, "Who were the Shudras?" is not attributed to him. Vinayak Damoder Savarkar: A prominent figure in the Hindu nationalist movement, known for his concept of Hindutv(A) His notable works include 'The Indian War of Independence 1857' and 'Hindutva: Who Is a Hindu?'. This specific book is not by him. Dr. Babasaheb Ambedkar: An eminent Indian jurist, economist, social reformer, and political leader who was the principal architect of the Constitution of Indi(A) He campaigned against social discrimination towards Dalits and supported the rights of women and labor. He authored several scholarly works focusing on the caste system, untouchability, and the history of Indian society. Pt. Sundarlal Sharma: A freedom fighter and social reformer from Chhattisgarh, who worked against untouchability. While important, he is not known for authoring this specific historical-sociological text.
Step 3: Confirm the authorship of "Who were the Shudras?".
"Who Were the Shudras? How They Came to Be the Fourth Varna in the Indo-Aryan Society" is a critically acclaimed historical and sociological work published in 1946. It was written by Dr. (B)R. Ambedkar. In this book, Ambedkar critically examines the historical origins and evolution of the Shudra varna (the fourth varna in the Hindu social hierarchy).
The final answer is $\boxed{\text{Dr. Babasaheb Ambedkar}}$.
