GATE 2023 BM – Question 63
A total hip-joint prosthesis has L₁=40 mm, L₂=60 mm, θ₁=45° and θ₂=90°, as shown. While the subject stands symmetrically on both feet, a joint reaction of 400 N acts vertically at the femoral head A. Calculate the magnitude of the moment about C in N m, to one decimal place.
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Correct answer: 11.0 to 12.0
Explanation
The moment equals force times perpendicular distance to its vertical line of action. Segment BC is vertical because θ₂=90°, so it contributes no horizontal offset. The horizontal distance from C to A is L₁cosθ₁=40cos45°=28.284 mm=.028284 m. Moment=400×.028284=11.3137 N m, or 11.3. The stated four-hundred-newton reaction is already the applied force; do not halve it again.