A beaker of height H is made up of a material whose coefficient of linear thermal expansion is 3 α . It is filled up to the brim by a liquid whose coefficient of volume expansion is 3 α . If now the beaker along with its contents is uniform

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A beaker of height H is made up of a material whose coefficient of linear thermal expansion is 3 α . It is filled up to the brim by a liquid whose coefficient of volume expansion is 3 α . If now the beaker along with its contents is uniformly heated through a small temperature T , the level of liquid will reduce by (Given, α T ≪ 1 )

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Correct answer: B. 3 α TH

Let A is cross - sectional area of a beaker Then, final cross - sectional area A ′ = A 1 + 6 α T Final volume of liquid V ′ = AH 1 + 3 α T Final height, H ′ = V ′ A ′ ⇒ H ′ = H 1 + 3 α T 1 + 6 α T ∼ H 1 - 3 α T Reduction in level, H - H ′ = 3 α TH

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