Answer:
The plants absorb water through the phenomenon of osmosis where water moved from area of high concentration to area of low concentration through a semi permeable membrane.
When the plant with roots was placed in a jar of red dye, the roots absorbed color water due to which the color of stem and leaves turned pink.
On the other hand, when plant with no roots was placed in the jar, the mechanism of absorbing water was removed since the roots were removed. That is why, the plant without roots could not absorb the colored water and remained green with no color change.