Under what condition will the nail not grow?

The correct answer is the condition where the matrix is damaged. The matrix, located under the base of the nail, is responsible for producing new nail cells. When the matrix is injured or compromised, it can severely affect or completely halt the production of new nail growth. This damage could be due to trauma, infection, or other health issues, preventing healthy nail development.

In contrast, hang nails, excessive cuticle, or short nail plates do not hinder nail growth at the source. Hang nails may be painful or unsightly, but they do not impede the matrix's function. While too much cuticle can sometimes make it challenging to maintain nail health, it does not stop the growth of the nail if the matrix is intact. Similarly, having a short nail plate is simply a cosmetic concern and does not affect the underlying process of nail growth. Therefore, the health of the matrix is crucial; when it is damaged, the entire nail growth cycle can be disrupted.