Physics quiz question: torque exerted on by post on hinged table

Physics 205A Quiz 5, fall semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 8.32

A uniform table, of length 0.80 m and mass 6.2 kg, is supported at two points; a hinge at the right end of the table, and a post located 0.20 m from the left end. The magnitude of the torque exerted by the post on the table, about the hinge is:
(A) 24 N·m.
(B) 36 N·m.
(C) 41 N·m.
(D) 1.2×10² N·m.

Correct answer (highlight to unhide): (A)

The table is in static rotational equilibrium about the hinge, such that the cw torque of the post on the table is balanced by the ccw torque of the weight force on the table (exerted downwards at the CG):

(cw τ) = (ccw τ),
τ_post = τ_w,
τ_post = w·ℓ,

where the weight w = m·g, and the lever arm ℓ_w = (L/2) = 0.40 m (as the CG is in the middle of the uniform table), such that:

τ_post = m·g·(L/2) = (6.2 kg)·(9.80 N/kg)·(0.40 m) = 24 N·m.

(Response (B) is (3/4)m·g; response (C) is (5/6)m·g·L; response (D) is (5/2)m·g·L.)

Student responses
Sections 70854, 70855
(A) : 9 students
(B) : 34 students
(C) : 4 students
(D) : 1 student

Success level: 18%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.56

Student responses
Section 72177
(A) : 5 students
(B) : 7 students
(C) : 0 students
(D) : 0 students

Success level: 41%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80