Subtopic: Overload safety devices used in farm machinery
Question Statement:
A vector F⃗ = 5î − 10ĵ + 8k̂ is passing through the origin of a 3-D frame. Considering the tendency of rotation in the counter clockwise direction as positive, the moment about a point A: (3, 4, 8) is
Options:
(A) −16î+112ĵ+50k̂
(B) 112î+16ĵ−50k̂
(C) 50î−112ĵ+16k̂
(D) −112î−16ĵ+50k̂
Official Answer Key:
D
Step-by-Step Solution & Explanation
Moment of a force about a point A = r⃗ × F⃗, where r⃗ is the position vector from A to any point on the line of action of F (take the origin, O). r⃗ = O−A = (0−3, 0−4, 0−8) = (−3,−4,−8).
M = r⃗ × F⃗ = |î ĵ k̂; −3 −4 −8; 5 −10 8|
i-component: (−4)(8)−(−8)(−10) = −32−80 = −112
j-component: −[(−3)(8)−(−8)(5)] = −[−24+40] = −16
k-component: (−3)(−10)−(−4)(5) = 30+20 = 50
M = −112î −16ĵ + 50k̂. Answer: (D). Verified symbolically (cross product computed independently).
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