A

Step 1: Apply Newton's second law for the mass M. The forces acting on the mass are the gravitational force (Mg down) and the tension (T up). Thus, the equation is: \( Mg - T = Ma \) where \( a \) is the acceleration of the mass.
Step 2: The wheel rotates due to the tension in the cord. The torque (\( \tau \)) about the axle O produced by the tension is given by: \( \tau = T \cdot R \). This is also related to the angular acceleration (\( \alpha \)) of the wheel: \( \tau = I \cdot \alpha \), where I is the moment of inertia.
Step 3: Since the linear acceleration (\( a \)) of the mass and the angular acceleration (\( \alpha \)) of the wheel are related by \( a = R \cdot \alpha \), we can express \( \alpha \) as \( \alpha = \frac{a}{R} \).
Step 4: Substitute \( \alpha \) in the torque equation: \( T imes R = I rac{a}{R} \), leading to \( T = \frac{I a}{R^2} \).
Step 5: Substitute \( T \) back into our first equation: \( Mg - \frac{I a}{R^2} = Ma \)
Step 6: Rearrange to find a: \( Mg = Ma + \frac{I a}{R^2} \)
\( Mg = a \left( M + \frac{I}{R^2} \right) \)
Step 7: Solve for a: \( a = \frac{Mg}{M + \frac{I}{R^2}} \).
Step 8: Substitute a back into the tension equation: \( T = \frac{I a}{R^{2}} = \frac{I}{R^{2}} \cdot \frac{Mg}{M + \frac{I}{R^2}} \)
Therefore, Tension T can be clearly expressed with specific values for M, I, and R, resulting in the final formula. Tension depends directly on gravitational force and inversely on the moment of inertia as modified by the radius squared.