A uniform light slender beam $\text{AB}$ of section modulus $\text{EI}$ is pinned by a frictionless joint $A$ to the ground and supported by a light inextensible cable $\text{CB}$ to hang a weight $W$ as shown. If the maximum value of $W$ to avoid buckling of the beam $\text{AB}$ is obtained as $\beta \pi^{2} EI$, where $\pi$ is the ratio of circumference to diameter of a circle, then the value of $\beta$ is

1. $0.0924\:m^{-2}$
2. $0.0713\:m^{-2}$
3. $0.1261\:m^{-2}$
4. $0.1417\:m^{-2}$