Which of the following diseases is recognized as a root and stalk disease in grain sorghum?

Fusarium stalk rot is recognized as a root and stalk disease in grain sorghum because it is caused by the Fusarium fungus, which can infect the plant through the root system and then progress up into the stalk. This disease is characterized by the rotting of the stalk and can lead to significant losses in grain yield and quality due to weakened plant structures, making the plants more susceptible to lodging.

In contrast, the other options listed address different types of diseases or infections that do not primarily affect the root and stalk system in the same way. Bacterial stripe is primarily a leaf disease affecting the plant's foliage, while gray leaf spot and powdery mildew also mainly impact the leaves of the plant. Recognizing the specific diseases that affect different plant parts is crucial for proper management and control strategies in grain sorghum farming.