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A uniform wooden plank of length 1 m and specific gravity 0.5 is hinged at one end to the bottom of a tank. The tank is filled with water to a height of 0.5 m. Find the angle theta (in degrees) that the plank makes with the vertical in its equilibrium position (excluding theta = 0). Express your answer as x, where theta = 15*x degrees.
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Correct answer: 3
Solution
Torque balance about the hinge gives cos²(theta) = 0.5, so theta = 45 degrees. Since theta = 15x, x = 3.
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