How can you measure the plant pieces to determine the rate of osmosis?

By measuring the plant's pieces mass, or the surface area to volume ratio.

By measuring the change in mass from initial to after solution indicates the net flow of water, if it increases it proves that osmosis occurred.
If the surface area to volume ratio decreases that also means that osmosis has occurred.

This measurements can’t be used to determine the rate of osmosis but can  prove that it occurred.

the glands which are associated with each description is given below:

pancreas - is an endocrine and exocrine gland that secretes juices with enzymes for digestion. salivary glands- with protection and digestion in the mouth. liver- secretes bile for digestion.   lachrymal glands - secrete tears to moisten eyes and protect them from particles and infection.   sweat gland -regulates water, salt, and temperature. oil glands - to form a protective barrier on the skin.   goblet cells - secrete mucus for protection.