A solid floats with 84% of its volume immersed at 50°C and 88% immersed at 100°C. Estimate the liquid’s volumetric expansion coefficient in units of 10⁻³ °C⁻¹.
Physics · Mixed Chapter
JEE Main Practice

Question

A solid floats with 84% of its volume immersed at 50°C and 88% immersed at 100°C. Estimate the liquid’s volumetric expansion coefficient in units of 10⁻³ °C⁻¹.

G1 Physics · Accepted Answer

Step 1: For flotation, submerged fraction f=ρbody/ρliquid. Treat solid’s thermal expansion as negligible. Step 2: Thus ρ₁₀₀/ρ₅₀=f₅₀/f₁₀₀=0.84/0.88. Step 3: As ρ∝1/V, V₁₀₀/V₅₀=0.88/0.84≈1.04762. Step 4: β≈(1.04762−1)/50≈9.52×10⁻⁴≈1×10⁻³ °C⁻¹.