Adverbs and sentences that express a result state

Hi, everyone.
I have questions to ask native speakers of English, about adverb position in sentences like:

(1a) We gently rolled the ball down the hill.
(1b) We rolled the ball gently down the hill.

In (1), it appears that there is a subtle meaning difference between (1a) and (1b), namely, (1a) means that the action which caused the rolling motion was gentle, whereas (1b) means that the rolling motion itself was gentle.


On the basis of the difference in (1), please tell me whether the following sentences that express a result state are correct.

(2a) She immediately boiled these vegetables to a pulp.
(2b) She boiled these vegetables immediately to a pulp.

Are (2a,b) grammatical? If these are grammatical, do you feel the meaning difference like (1)? ; (2a) means that her action which caused the state change of vegetables was immediate, whereas (2b) means that the process in which vegetables changed to a pulp was immediate.


In the same way, are (3-4) grammatical, too? If so, do these sentence have the the meaning difference, as shown above?

(3a)He gently pounded the metal flat.
(3b)He pounded the metal gently flat.

(4a)The dog immediately barked the children awake.
(4b)The dog barked the children immediately awake.

Particularly, In (4), I intend to the below meanings.

1. Both sentences express that the dog barked so that the children awoke.
2. Especially, (4a) means that bark action was immediate, whereas (4b) means that the children immediately awoke.

but, I think (4b) ungrammatical.


Thanks in advance!

(1a) We gently rolled the ball down the hill. (1b) We rolled the ball gently down the hill. In (1), it appears that there is a subtle meaning difference between (1a) and (1b), namely, (1a) means that the action which caused the rolling motion was gentle, whereas (1b) means that the rolling motion itself was gentle.

Hmm.  I wouldn't have said so.  Whoever said that must have an overactive imagination!

As stated above, 3b and 4b are so awkward that they are unusable.

CJ

if the adjectives in (3-4b) are replaced with prepositional phrases like (1-2b), will the sentences like (3-4b) become more grammatical?

They are only slightly better when the prepositional phrases are used.  The thing is, the adverb belongs at the beginning of the verb phrase or at the end.  Squeezing it into places where it doesn't usually go is normally reserved for artistic literary writing or poetry.

He immediately drank himself into a stupor.
He drank himself into a stupor immediately.
He drank himself immediately into a stupor.  [Least usual.]

pounded and gently don't go together.  Allow me to change the adverb.

He quickly pounded the stone to pieces.
He pounded the stone to pieces quickly.
He pounded the stone quickly to pieces.  [Least usual.]

That said, each case must be judged individually on the basis of semantics.  (You seem to want a purely syntactic rule, and I'm afraid there isn't one -- just general guidelines.)

CJ