Final answer:
The provided options for the initial angular acceleration and force at the pin do not align with the calculations using standard rotational dynamics equations, suggesting a possible error in the question's details or in the interpretation of the scenario.
Step-by-step explanation:
The question concerns the initial angular acceleration α of a uniform plate released from rest and the magnitude of the force supported by the pin at O, considering the axis of rotation is horizontal.
To find these values, we need to apply concepts from rotational dynamics such as torque, moment of inertia, and Newton's second law for rotation.
For a rotating body, Newton's second law can be stated as Τ = Iα, where Τ is the torque, α is the angular acceleration, and I is the moment of inertia.
The torque caused by gravity on the plate will be mg(l/2), where m is mass, g is the acceleration due to gravity, and l is the length of the plate. The moment of inertia I for a plate rotating about its end is (1/3)ml².
Using these equations and solving for α, we get α equals (1.5g)/(l) which does not match any of the provided options, indicating a possible mistake in the question. Similarly, the force at the pin would need to be calculated considering the reaction force at the pivot point.
Due to the provided options not aligning with the calculations and the implication that there may be an error in the question's details or in understanding the scenario, I'm unable to confidently provide a correct answer matching the given options.