Equivalent systems of parallel forces

Steps:

• Identify the resultant force as the vector sum of all forces in the pair.
• Calculate the torque by summing moments about a reference point, using torque = force × perpendicular distance.
• For pair X, assume two 10 N forces leftward, separated by 0.5 m, yielding 20 N left and 10 Nm clockwise torque.
• For pair Y, assume configuration leading to 20 N left but 30 Nm anticlockwise torque.

Why A is correct:

• Matches the definition of equivalent system: resultant force (20 N left) and net torque (10 Nm clockwise) per Varignon's theorem for parallel forces.

Why the others are wrong:

• B: Incorrect torque magnitude and direction for X.
• C: Applies Y's torque to Y but mismatches X's details.
• D: Ignores the resultant force of 20 N left for Y.

Not enough information: Diagram absent, assumptions based on choices.

Final answer: A