**Explanation:**

The correct answer is option 'D': The food is ground by mandibles and gizzard.

**Mandibles and Gizzard:**
Cockroaches have a pair of strong, sharp mandibles that are used for biting and chewing their food. The mandibles help them to break down larger food particles into smaller pieces, making it easier to digest. After the food is bitten and chewed by the mandibles, it passes into the gizzard.

The gizzard is a muscular organ that is located in the digestive system of the cockroach. It contains small, hard particles called gastric mill that help in grinding the food further. The contraction of the gizzard muscles helps to grind the food into smaller particles, increasing the surface area for digestion. The grinding action of the gizzard, along with the digestive enzymes present in the gut, helps in the breakdown of food into simpler substances.

**Other Options:**
Let's analyze the other options to understand why they are incorrect:

a) Malpighian tubules are excretory organs that project out from the coelom.
This statement is incorrect. Malpighian tubules are excretory organs found in insects, including cockroaches. They are not projected out from the coelom, but instead, they are blind-ended tubules that are connected to the digestive system. They function in the removal of nitrogenous waste from the body.

b) Oxygen is transported by hemoglobin in blood.
This statement is incorrect. Hemoglobin is a respiratory pigment found in the blood of vertebrates, including humans. It is not present in the blood of insects like cockroaches. Instead, cockroaches have a network of tiny tubes called tracheae that directly transport oxygen to their tissues. The tracheal system is responsible for the respiratory gas exchange in insects.

c) Nitrogenous excretory product is urea.
This statement is incorrect. Cockroaches, like most insects, excrete nitrogenous waste in the form of uric acid. Uric acid is a relatively insoluble compound that requires less water for its excretion. This adaptation helps insects to conserve water in their arid environments.

Therefore, option 'D' is the correct answer as it accurately describes the mechanism by which cockroaches grind their food using mandibles and a gizzard.