The correct option is The Damodar.
Explanation
The question describes a river based on its geological structure (rift valley), drainage terminus (Hugli), historical impact ("Sorrow of Bengal"), and associated river valley development (multipurpose project).
Detailed Analysis:
- Rift Valley: The Damodar River originates in the Chotanagpur Plateau of Jharkhand. It flows through a geological rift valley, a structural trough that directs its course eastward. This is a distinct feature shared with rivers like the Narmada and Tapi, though the Damodar flows east.
- Joins the Hugli: The Damodar is a major tributary of the Hugli River (a distributary of the Ganga). It joins the Hugli approximately 48 km below Kolkata.
- "Sorrow of Bengal": Historically, the river was infamous for devastating floods in the plains of West Bengal, earning it the epithet "Sorrow of Bengal."
- Multipurpose Project: To mitigate these floods and harness water for irrigation and electricity, the Damodar Valley Corporation (DVC) was established in 1948. It was the first multipurpose river valley project of independent India, modeled on the Tennessee Valley Authority (TVA) of the USA.
Incorrect Options:
- The Mahananda The Mahananda: This is a Himalayan river rising in Darjeeling. It joins the Ganga (Padma) in Bangladesh and does not flow through a rift valley.
- The Subarnarekha The Subarnarekha: While it rises in the Chotanagpur Plateau near Ranchi, it flows independently into the Bay of Bengal and is not a tributary of the Hugli.
- The Rupnarayan The Rupnarayan: It is a tributary of the Hugli, but it is not associated with the specific "Sorrow of Bengal" title or the extensive rift valley geology in the same context as the Damodar.
Key Takeaway: The Damodar River is a Peninsular river that flows through a rift valley, joins the Hugli, and hosts India's first multipurpose river valley project (DVC), which transformed it from the "Sorrow of Bengal" into a resource for the region.