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A uniform cylinder of length L, mass M and cross-sectional area A hangs vertically from a fixed support by a light spring of force constant k. At equilibrium the cylinder is half immersed in a liquid of density sigma. Find the extension x0 of the spring at this equilibrium position.
- Mg/k
- (Mg/k) (1 - LAσ/M)
- (Mg/k) (1 - LAσ/2M)
- (Mg/k) (1 + LAσ/M)
Correct answer: (Mg/k) (1 - LAσ/2M)
Solution
At equilibrium the upward spring force k*x0 plus the upward buoyant force balance the weight Mg. The submerged volume is half the cylinder, A*L/2, so buoyancy = (A*L/2)*sigma*g.
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