Torque equilibrium for a uniform bar

Steps:

• Weight W acts at center (L/2 from end A); X at L/4 from A, Y at L from A.
• Vertical force balance: Rx + Ry = W.
• Take torques about X: W acts L/4 to right (clockwise torque W·L/4).
• Ry acts 3L/4 to right (counterclockwise torque Ry·3L/4); set equal: Ry·3L/4 = W·L/4.
• Solve: Ry = W/3, Rx = 2W/3, so Ry/Rx = 1/2.

Why A is correct:

• Torque balance about X directly yields Ry/Rx = 1/2 via the lever arm ratio (distance to W : distance to Ry = 1:3).

Why the others are wrong:

• B: 1/3 ignores torque; confuses with Ry/W.
• C: 3/5 from misplacing center or supports.
• D: 2/5 swaps Rx/Ry ratio.

Final answer: A