Final answer:
Tensions arose after Muhammad's death regarding leadership and inheritance. Two primary claimants for leadership emerged: Ali ibn Abi Talib and Abu Bakr. The Arab tribes believed that the community's purpose had been completed, but Muhammad's accomplishment in uniting them under Islam was not intended to be temporary.
Step-by-step explanation:
Tensions arose after Muhammad's death not just over leadership and inheritance, but also over whether the alliance was ever intended to last beyond its founder. Some Arab tribes left to return to their homes, while others may have believed they could discard their commitment to the worship of the one God and membership.
In many tribal- and clan-based societies like that of the Arabs, leadership was not hereditary. As Muhammad was dying, two primary claimants for leadership emerged: his son-in-law Ali ibn Abi Talib, and a friend and confidant of Muhammad's named Abu Bakr.
Ali, related to the Prophet by blood and marriage, claimed to have been chosen by Muhammad as his heir and successor. Abu Bakr, on the other hand, was one of the elders of the community, well respected and popularly chosen. Both had been among the first to convert to Islam.
When Muhammad died, questions about the leadership of the community arose. Who was capable of leading the community, and what had Muhammad accomplished by uniting the Arab tribes? The first few years following Muhammad's death tested the community's resolve.
The Arab tribes believed that the community's purpose had been completed. However, Muhammad's accomplishment in bringing people together under Islam was not intended to be temporary. This led to tensions and divisions within the community.