GATE 2026 BM – Question 60
An arm holds a ball in static equilibrium, as shown. Biceps force F acts at 60° to the rigid lower arm. Ball weight W1=50 N and lower-arm weight W2=20 N. The biceps attaches 4 cm from elbow O, W2 acts another 12 cm along, and W1 another 16 cm beyond W2. Find F in N, nearest integer.
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Correct answer: 550 to 560
Explanation
Take moments about elbow O, eliminating its reaction forces. Perpendicular biceps component is F sin60° at 0.04 m. The weights act at 0.16 and 0.32 m. Thus 0.04F sin60°=20×0.16+50×0.32=19.2 N m. Therefore F=19.2/(0.04 sin60°)≈554.26 N, rounded to 554 N.