The Mahatma Gandhi Hydroelectric Project is located on the Sharavati River. The key here is to understand that the project is a hydroelectric project, which means it utilises the natural flow of water to generate electricity.

When looking at the options, we can eliminate options 1, 3, and 4 (Godavari, Cauvery, and Krishna) as they are not associated with the Sharavati River.

This leaves us with option 2, Sharavati, which is the correct answer. The Sharavati River is located in Karnataka, India and is known for its hydropower potential. The Mahatma Gandhi Hydroelectric Project harnesses the power of the Sharavati River to generate electricity.

In conclusion, the Mahatma Gandhi Hydroelectric Project is located on the Sharavati River. It is important to understand the concept of hydroelectricity and its reliance on rivers or water bodies for generating power.