Tape recorder head has only 2 pins, which one is for grounding?
There is a lot more to a tape player than just the tape head.  Tape heads are not meant to connect directly to a regular preamp or even a microphone input.

The proper circuit inside a tape player would probably consider the output of the tape head a differential signal.  The head's case would be grounded, and the two coil connections treated as equally as possible until after the differential to single ended conversion.  After that there will be some frequency shaping and amplification to line level.  Only then is the signal ready to be connected to other equipment that the jack you show would plug into.

A tape head and a plug are a long way from a tape player.

Just because you wire a signal to a standard plug doesn't mean that signal magically has the characteristics of what the plug is intended to carry.

Added

Apparently you already have a sound source, and want to "inject" that into a existing tape player so that the tape player thinks it's playing a tape but is actually playing the signal the tape head is being artificially stimulated with.  That's such a bizarre thing to want to do that I didn't realize that's what you wanted on initially reading your question.

The first obvious solution is to not try to fake out the tape player.  This player most likely puts out a line level audio signal that goes to a power amp somewhere.  Tap into that directly.  Your iPod should be able to drive that.

If you really really want to go this bizarre route, then you can drive the tape head you have from the iPad output and hold it right up against the pickup head in the tape player.  However, there will be some problems with this:

The frequency response will be a mess.  The signal written to magnetic tape deliberately has the high frequencies emphasized.  This is so that high frequencies can be attenuated on reading, which helps with overall signal to noise ratio.  The same thing was done with old vinyl records, although the frequency profile are different between the two.  It's been many years since I've dealt with audio tape electronics, but vaguely remember that the tape head frequency profile was called something like the "NAB" standard, and that for records the "RIAA" standard.

Getting the drive level right will be tricky.  The tape head probably has higher impedance than what the iPad is intended to drive, so the iPad won't care.  The tape head itself is just a electro magnet electrically, so it should be easily able to take the little power the iPad can put out.  However, the pickup signal from a real tape head is quite small, and it will be easy to overdrive the pickup head in the tape player.  The coupling will also vary significantly with the placement and size of gap between the two heads.



You might be able to kludge this up if you look up the appropriate frequency shaping (NAB standard?), then add appropriate resistors and capacitors between the iPad output and the tape head.

Again, tapping into the line level audio signal between the tape player and the power amp makes a lot more sense.