1. It is of no use to cry like a baby.

2. It is no use crying like a baby.
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Are both the same and grammatical?
Is 'it' a false subject? Is 'to cry like a baby' and 'crying like a baby' a real subject?

#1 is incorrect, but would be better if you use "crying" instead of "to cry."

#2 is correct.

"It" is the subject.
http://learnenglish.britishcouncil.org/en/english-grammar/pronouns/it-and-there

Both sentences are grammatically correct, but they have slightly different structures and connotations.

In the first sentence, "It is of no use to cry like a baby," the word "it" is a pronoun serving as a dummy subject. It doesn't refer to anything specific, but it is used to introduce the existential clause "is of no use." The real subject is the infinitive phrase "to cry like a baby," which functions as the subject complement. This sentence implies that crying like a baby is not beneficial or helpful.

In the second sentence, "It is no use crying like a baby," the word "it" is again a pronoun serving as a dummy subject. The real subject is the gerund phrase "crying like a baby," which functions as the subject complement. This sentence also conveys the same meaning as the first one, suggesting that crying like a baby is futile or pointless.

So, both sentences have the same overall meaning, but they differ slightly in structure. The use of "it" as a dummy subject in both sentences is a common construction in English.