A splash of knowledge

While the glass is suspended by the string and stationary the net force is zero. Therefore the string tension is equal in magnitude to the gravitational force. The gravitational force is $F_g=(m_w + m_g) g$ . The mass $m_w$ of the water is $\rho V_w$ where $\rho$ is the density in $kg/m^3$ if we use SI units. The volume of water is just $\pi r^2 h=\pi \times 0.04^2 \times 0.1=0.0005~m^3$ . The mass of the water is therefore $1000 \times 0.0005=0.5~kg$ . The total gravitational force when the string breaks is therefore $(0.5 +0.1)9.8=5.88~N$ , which is also the maximum tension.