The correct answer for the reason or ground for the British Empire to annex Sambalpur in 1850 is option 2, which states that the death of its ruler without any heir was the cause. This means that when the ruler of Sambalpur passed away, there was no direct successor to take his place. In such cases, the British Empire often saw an opportunity to take control and annex the territory. The absence of a clear heir allowed the British to claim that they were stepping in to maintain order and prevent any potential conflicts over succession. This tactic was commonly used by the British Empire to expand their dominion and exert control over various regions.