Discussion

Answer: A

The correct free body diagram of the lever is (A), as the key states.

The lever RS carries the applied force \(F\) downward at R. It rests against the left drum at T and against the right drum at U, and its foot S stands on the ground. The drums are smooth and the lever-drum friction is negligible, so each drum can push on the lever only perpendicular to it. The lever lies on the upper-right side of the left drum's centre, so at T the drum pushes the lever up and to the right (\(N_{1}\), perpendicular to the lever). The lever lies on the lower-left side of the right drum's centre, so at U that drum pushes the lever down and to the left (\(N_{2}\), also perpendicular). At S the ground gives a vertical reaction \(N_{3}\) and a horizontal friction force \(F_{f}\), because the problem makes only the drum-lever friction negligible and the unequal pushes at T and U have a horizontal component to be balanced.

(B) draws \(N_{1}\) vertical, but a smooth contact force must be perpendicular to the lever. (C) applies \(N_{2}\) at the foot S instead of at the contact point U. (D) leaves out the friction force at S. Only (A) has \(N_{1}\) at T and \(N_{2}\) at U perpendicular to the lever, with both \(N_{3}\) and \(F_{f}\) at S. The choice among the diagrams follows the printed arrows; I read them on the page image and did not find a published solution to compare against.