Solution:

The mass of the negatively charged sphere increases because:

• When a sphere becomes negatively charged, it gains extra electrons. Since electrons have mass ($9.1 \times 10^{-31} \, \text{kg}$), the addition of electrons increases the mass of the negatively charged sphere.
• Conversely, the positively charged sphere loses electrons, resulting in a slight decrease in its mass.

Thus, the mass of the negatively charged sphere increases due to the addition of electrons.