A uniform beam of mass 5 kg is hinged to a wall and supported at its outer end by a wire as shown. The outer end supports a 10 kg load, also shown: The tension in the wire is:

Question

BlackTom AI · Accepted Answer

To tackle this problem, focus on rotational equilibrium about the hinged wall.
Option A: 245 N. This would arise if you computed the torque balance as T_y × L = g(5 × L/2 + 10 × L) but used sin(36.9°) = 0.5 instead of the actual value. Since sin(36.9°) is about 0.6, using 0.5 leads to an overestimate of T by a factor of 0.5/0.6, yielding roughly 245 N. This shows a misapplication of the angle or an incorrect trigonometric value.
Option B: 122.5 N. This would occur if you divided the vertical component torque by 2 or forgot to include the angle’s sine properly, or if you canceled L incorrectly. In reality, the vertical component of the tension must balance the total weight torque, which requires dividing by sin(36.9°), not by 2, so 122.5 N is too small for the given geometry.
Option C: "impossible to calculate without knowing the length of the beam." In torque problems of this type, the beam length L cancels out when you equate the torques about the hinge, because every torque term contains L as a factor (W × distance and T_y × L). Thus length is not a missing ingredient here; you can compute T without knowing L.
Option D: 204 N. This result comes from setting the counterclockwise torque by the vertical component of the tension equal to the clockwise torques from the weights. The beam weighs 5g acting at L/2 and the 10 kg load weighs 10g at L, so total weight torque is g(5×L/2 + 10×L) = g×12.5×L. The tension’s vertical component is T sin(36.9°) acting at distance L, giving T sin(36.9°) × L. Equating gives T = g×12.5 / sin(36.9°). With g ≈ 9.8 m/s² and sin(36.9°) ≈ 0.6, T ≈ 9.8×12.5 / 0.6 ≈ 204 N, matching this option.

Overall, options A and B stem from misusing the angle or the torque relation, option C is incorrect because L cancels out in the torque balance for this setup, and option D correctly applies rotational equilibrium to yield about 204 N.

A uniform beam of mass 5 kg is hinged to a wall and supported at its outer end by a wire as shown. The outer end supports a 10 kg load, also shown: The tension in the wire is:

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