The most important difference resides in the difference in fiber, carrots fibers are mostly composed by cellulose which is rigid, while apples are composed by hemicellulose and pectine which are not as rigid.
While water fills an important part in rigidity, you must take into account how much of that water is Aw(available water) and how much is deeply embedded in the rest of the components.
Most of the fibers in apples are in its coating, while it is most equally distributed in carrots. That’s also why you feel more resistence in carrots.
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