Final answer:
Hard hats should be worn in environments with potential head injury risks such as construction sites, industrial plants, and mining operations, but are not typically required in office buildings.
Step-by-step explanation:
Hard hats are an essential part of personal protective equipment (PPE) in various work environments. They are designed to protect the head from injuries due to falling objects, impacts, and other hazards that are common in certain work settings. Among the options provided, hard hats should be worn on construction sites, in industrial plants, and during mining operations where the risk of head injury is significant due to the nature of the work. However, they are generally not required in office buildings where such hazards are minimal, and the environment does not typically pose the same level of risk for head injuries. Ensuring that the correct safety gear is worn in appropriate situations is crucial, following the standards set by organizations such as the Occupational Safety and Health Administration (OSHA).