Please tell which one is correct. I am much interested. Or I am very Interested. Please explain scientifically.
"I am very interested" is correct.
"I am much interested" is in a grey area. It will sound odd to most people. Speakers tend to avoid using "much" in affirmative clauses, although it is used in interrogatives, negatives, and when qualified as "very much" (see http://dictionary.cambridge.org/grammar/british-grammar/adverbs-of-degree/much-a-lot-lots-a-good-deal-adverbs ).
A small number of expressions sound OK and are idiomatic with affirmative "much". For example, "I am much obliged". These expressions just have to be learnt on a case-by-case basis.
By contrast, "I am much disappointed", "I am much happy", "he is much silly" sound extremely awkward and borderline ungrammatical. "Very disappointed", "very happy", "very silly" would be the accepted forms.
You can say "Do you like the film much?" and "I don't like the film much". But you can't say "I like the film much".
You can say "I like the film very much", "I like the film so much" and even "I like the film too much", but "much" on its own doesn't work in affirmatives. In these cases, of course, "very" wouldn't work as a substitute - instead, the substitute would be "a lot": "I like the film a lot".