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A uniform wooden plank of length 1 m is hinged at its lower end to the bottom of a tank. The tank holds water to a depth of 0.5 m. The plank's specific gravity is 0.5. Find the angle theta the plank makes with the vertical (or as defined) in its equilibrium floating position.
- theta = 45 deg
- theta = 30 deg
- theta = 60 deg
- theta = 0 deg (plank vertical)
Correct answer: theta = 45 deg
Solution
Balancing torques about the hinge: weight acts at the plank center, buoyancy acts at the center of the submerged portion. The submerged length is h/cos(theta) with h = 0.5 m water depth. Using specific gravity 0.5 leads to cos²(theta) = 1/2, giving theta = 45 deg.
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