What is the variation ∆h in the height of the liquid column? The formula for the new volume of the liquid column is V = V0(1 + β∆T) = Ah. The form...

Using the formula V = V0(1 + β∆T) = Ah, we can find the variation ∆h in the height of the liquid column by isolating ∆h: V = Ah V0(1 + β∆T) = A(h + ∆h) V0 + V0β∆T = Ah + A∆h V0β∆T = A∆h ∆h = V0β∆T/A Substituting the given values, we have: ∆h = (V0β∆T)/A = (V0β)/A = (πr²hβ)/A Using the formula A = A0(1 + 2α∆T), we can find A: A = A0(1 + 2α∆T) = πr0²(1 + 2α∆T) Substituting the given values, we have: A = π(0.5 cm)²(1 + 2(1.2 x 10^-5 cm^-1)(1°C)) = 0.7854 cm² Substituting A and β into the previous equation, we have: ∆h = (πr²hβ)/A = (π(0.5 cm)²(10 cm)(2.1 x 10^-4 cm^-1))/0.7854 cm² = 1.62 mm Therefore, the correct answer is option b) 1.62 mm.