The correct answer is option 1, Bal Gangadhar Tilak. He was the one who set up the Home Rule League at Poona.

Now let`s analyze the other options.

Option 2, Gopal Krishna Gokhale, was a prominent political leader during the Indian independence movement. However, he did not set up the Home Rule League at Poona.

Option 3, Mahadev Govind Ranade, was a social reformer and a close associate of Gopal Krishna Gokhale. However, he was not associated with the establishment of the Home Rule League at Poona.

Option 4, Vinoba Bhave, was a social reformer and follower of Mahatma Gandhi. He was not involved in the establishment of the Home Rule League at Poona.

Therefore, option 1, Bal Gangadhar Tilak, is the correct answer. He was a prominent figure in the Indian independence movement and played a crucial role in advocating for self-rule and Swaraj (self-governance) in India. The Home Rule League was a political organization founded by him in 1916 to demand self-rule from the British colonial government.