Final answer:
The bits of pigment found in the cortex of a hair are known as melanin granules, and they determine the hair's color.
Step-by-step explanation:
The term for bits of pigment found in the cortex of a hair is melanin granules. In hair, melanin is responsible for the pigmentation and can come in two forms: eumelanin, which provides black and brown colors, and pheomelanin, which gives hair a red color. Hair color varies due to the type and amount of melanin present, which is determined genetically. As we age, melanin production decreases, often resulting in hair turning gray or white.