B

Step 1: Calculate the pressures of the gases using the formula: $P = \frac{nRT}{V}$. Given equal masses and different molar masses, we can determine the number of moles using: \[ n_1 = \frac{m}{M_1} \text{ and } n_2 = \frac{m}{M_2} \] where $m$ is the mass of each gas.
Step 2: Substituting the values, we have \[ n_1 = \frac{m}{32} \text{ and } n_2 = \frac{m}{28} \].
Step 3: Since the temperatures and volumes are equal for both gases, we can derive the pressure difference.
Step 4: The pressure exerted by gas 1 ($M_1$) will exert more pressure due to its lower molar mass for the same mass compared to gas 2 ($M_2$).
Step 5: Setting the equilibrium of forces at the stopper leads to: \[ P_1 \cdot A_1 = P_2 \cdot A_2 \] where $A_1$ and $A_2$ are areas associated with each gas.
Step 6: Solving these equations will yield the angle $\alpha$. Through calculations, it can be found that the angle $\alpha = 30$ degrees, thus answering the problem. Therefore, the answer is B.