The answer shud be A ,

1) here it logically explains that cyclist is going to set a record : - correct
2) here that is referring to power , it seems as if power is going to set a record : wrong
3) hopefully is not recommended in GMAT , here what does this referring to : wrong
4) here the term power shud be considered as it is the one helping cyclist to set a record , distorts meaning : wrong
5) here the term power shud be considered as it is the one helping cyclist to set a record , distorts meaning : wrong

B - "provide enough power that will set" is unidiomatic. Better to say "enough power to set"
C - You have two independent clauses here: "An unusually strong...enough power" and "this will set a...fiber and plastic". Yet, only a comma connects the two. No good! You must have a conjunction or semicolon there to "glue" the two clauses together. A comma alone is never enough.
D - This is unidiomatic, too. Better to say "hopes to set." Also, this construction changes the meaning of the sentence -- the focus now is on a particular cyclist setting a record, whereas in the original sentence the issue was about enough power being generated by a cyclist in order to set the record.
E - Change in meaning as in D. Also, "hopes to set" over "hopes setting".

The correct answer is A.

Let's replace option D in original sentence and remove middlemen.
[strike]An unusually strong[/strike]cyclist is hopeful to set a [strike]new distance[/strike] record for [strike]human-powered[/strike] aircraft in [strike]MIT’s[/strike] diaphanous construction [strike]of graphite fiber and plastic[/strike].

cyclist is hopeful to set record for aircraft in MIT’s diaphanous construction.

Lets simplify original sentence.
It is hoped,[strike]An unusually strong[/strike] cyclist can provide [strike]enough[/strike] power to set [strike]a new distance[/strike] record for [strike]human-powered[/strike] aircraft in MIT’s diaphanous construction[strike]of graphite fiber and plastic[/strike].

It is hoped that cyclist can provide power to set record for aircraft in MIT’s diaphanous construction

Changes in meaning:
Cyclist himself is hopeful, whereas in orginal sentence nothing mentioned about cyclist's hope, it is hoped by somebody else such as people or some group.

If any question, please revert.

I hope my explanation helped, if indeed please give me kudos.

For me, the clear candidates are options A and E.

I discarded E because it changes the meaning. It is not the same to say in an impersonal manner "it is hoped", as the original sentence is saying, than to say "the cyclist hopes setting".

In this latter case, we would be saying that it is the cyclist who hopes to set a new record.

Do you agree with my observation?

This explanation is alright - additionally hope + infinitive is preferred to hope + gerund.... added OA.

Here is my explanation:

(A) can, it is hoped, provide enough power to setcorrect
(B) it is hoped, can provide enough power that will setThat refers to power...power wont set the record. And "An unusually strong cyclist it is hoped" is not grammatical
(C) hopefully can provide enough power, this will set"This" is not preferrable to use as a subject in gmat
(D) is hopeful to setchanges the meaning...it says the cyclist is hopeful
(E) hopes settingsame as D...changes the meaning

An unusually strong cyclist can, it is hoped, provide enough power to set a new distance record for human-powered aircraft in MIT’s diaphanous construction of graphite fiber and plastic.

X can provide Y is correct grammatical usage..

IMHO with (A) , errors in my opinion with other options marked in RED..
_________________

A seems fine..but the "it is hoped" kind of not really...
can X TO -> shows purpose. B uses THAT - so the purpose is changed.
C - enough power for what? Not good
D - changes the meaning...a cyclist is hopeful...not correct
E - a cyclist hopes - not correct.

B, C, and E all use the incorrect verb tense.

D is awkward and changes the meaning of the sentence. Plus it can be shortened to "A cyclist to set a new..."