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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Thermal Properties of Matter

NTA Abhyas 2020 · Physics · Thermal Properties of Matter

A beaker of height H is made up of a material whose coefficient of...

A beaker of height HH is made up of a material whose coefficient of linear thermal expansion is 3α3 \alpha. It is filled up to the brim by a liquid whose coefficient of volume expansion is 3α3 \alpha. If now the beaker along with its contents is uniformly heated through a small temperature TT, the level of liquid will reduce by (Given, \alphaT≪1\alphaT ≪ 1)

Options

  1. AαTH\alpha\text{TH}
  2. B3αTH3\alpha\text{TH}
  3. C9αTH9\alpha\text{TH}
  4. D6αTH6\alpha\text{TH}

Correct answer

B. 3αTH3\alpha\text{TH}

Step-by-step solution

Let A is cross - sectional area of a beaker

Then, final cross - sectional area

A^{′} = A[1+6αT]<br/><br/>Finalvolumeofliquid<br/><br/>\text{A} \left[1 + 6 \alpha \text{T}\right]<br /><br />Final volume of liquid<br /><br /> V^{′} = AH[1+3αT]<br/><br/>Finalheight,\text{AH} \left[1 + 3 \alpha \text{T}\right]<br /><br />Final height, H^{′} = V′A′\dfrac{V^{′}}{A^{′}}

⇒H′=H[1+3αT][1+6αT]⇒ H^{′} = \text{H} \dfrac{ \left[1 + 3 \alpha \text{T}\right]}{ \left[1 + 6 \alpha \text{T}\right]}∼ H[1−3αT]\text{H}\left[1 - 3 \alpha \text{T}\right]

Reduction in level, H−H′=3αTH\text{H} -H^{′} = 3 \alpha \text{TH}
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