Final answer:
To achieve a resultant couple of zero, the magnitude of p must be equal to the magnitude of the opposing momenta, and the direction must be exactly opposite (antiparallel).
Step-by-step explanation:
The question asks about the condition under which the resultant couple is zero and seeks the magnitude of p. To have a resultant couple of zero, the moments or torques must be equal and opposite to cancel each other out. According to the information provided, if two momenta, p₁ and p₂, are equal in magnitude and opposite in direction (antiparallel), their vector sum, and hence their resultant couple, would be zero. This is also true when momenta are parallel with equal magnitudes but opposite in sense, as the sin 0° = sin 180° = 0 which causes the vector product (or torque) to vanish; hence, the magnitude of p would need to be of equal value to the other momenta but directed oppositely or antiparallel to create a resultant couple of zero.
In a scenario where two vectors are equal in magnitude and opposite in direction, the magnitude of their resultant vector is zero, answering part 5 of the provided information. Overall, without specific values, we conclude that the magnitude of p must be equal to the magnitude of the opposing momenta for the resultant couple to be zero.