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A leak-proof cylinder of length 1 m, made of a material with negligible thermal expansion, floats vertically in water at 0 deg C with 20 cm of its length above the water surface. When the water temperature is raised to 4 deg C, the exposed length becomes 21 cm. The density of water at 4 deg C relative to its density at 0 deg C is closest to:
- 1.01
- 1.04
- 1.03
- 1.26
Correct answer: 1.01
Solution
For a floating cylinder of fixed mass and cross-section, rho_water * (submerged length) = constant. At 0 deg C submerged length = 100 - 20 = 80 cm; at 4 deg C = 100 - 21 = 79 cm. So rho₄/rho₀ = L_sub0/L_sub4 = 80/79 = 1.0126, which is approximately 1.01.
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