Two-Rod Stasis

Rod $1$ is $1 \, \text{m}$ long and has mass $M_1 = 1 \, \text{kg}$ . One end of Rod $1$ is attached to a wall with a hinged support, and the other end is free.

Rod $2$ is $1 \, \text{m}$ long and has mass $M_2$ . One end of Rod $2$ is attached to the wall with a fixed (rigid) support, and the other end is free. Rod $2$ is $1 \, \text{m}$ above Rod $1$ .

Ambient Earth gravity is $10 \, \text{m/s}^2$ downward. If the two rods are in stasis, and $M_2 = \sigma \times 10^{11} \, \text{kg}$ , what is the value of $\sigma$ ?

Details and Assumptions:
- The universal gravitational constant is required, in addition to Earth gravity. $G = 6.67 \times 10^{-11}$
- The hinged support for Rod $1$ can supply horizontal and vertical forces, but it cannot supply moments
- Both rods are rigid and uniform