To help strengthen your index finger, try barreing with just that finger, dont make the major chord shape. Start up on the 9th or 7th fret and when you can barre there with ease, holding down all strings, start moving down the board making sure you get all the strings until you reach the first - then you can play the F chord. The bad habit I developed was that I learnt the barre chord as a shape and didnt have the strenght of the barre on all strings. Its not a problem on the F-shaped chords but when you start playing more complicated barres then you need the strenght in every finger. A mate showed me this technique and the problem was fixed easily. Itll take you a while to get the strength but its makes things so much easier. itll help you whatever type of music you play.
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