The Damodar River, which flows through Jharkhand and West Bengal, has a long history of devastating floods due to its high discharge during the monsoon season.
Step 1: Analyze the options.
(A) Bihar: The Kosi River is known as the "Sorrow of Bihar" because of its frequent and destructive flooding.
(B) Assam: The Brahmaputra River is the primary cause of massive flooding in the state of Assam.
(C) West Bengal: The Damodar River was traditionally known as the "Sorrow of Bengal" because it caused frequent floods in the plains of West Bengal. To control this, the Damodar Valley Corporation (DVC) was established in 1948.
(D) Andhra Pradesh: Flooding in Andhra Pradesh is typically associated with the Godavari and Krishna rivers.
Step 2: Conclusion.
Historically and geographically, the Damodar River is the main cause of flooding in the state of West Bengal.
Final Answer:
\[
\boxed{(C) \, \text{West Bengal}}
\]