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Thermometry, Thermal Expansion and Calorimetry — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsThermometry, Thermal Expansion and Calorimetry1 Mark
MCQ
A vertical column $50 \mathrm{~cm}$ long at $50^{\circ} \mathrm{C}$ balances another column of same liquid $60 \mathrm{~cm}$ long at $100^{\circ} \mathrm{C}$. The coefficient of absolute expansion of the liquid is
  • ✓
    $0.005 /{ }^{\circ} \mathrm{C}$
  • B
    $0.0005 /{ }^{\circ} \mathrm{C}$
  • C
    $0.002 /{ }^{\circ} \mathrm{C}$
  • D
    $0.0002 /{ }^{\circ} \mathrm{C}$
✓

Answer

Correct option: A.
$0.005 /{ }^{\circ} \mathrm{C}$
$ \frac{h_1}{h_2}=\frac{\rho_1}{\rho_2}=\frac{\left(1+\gamma \theta_1\right)}{\left(1+\gamma \theta_2\right)}\quad\left[\because \rho=\frac{\rho_0}{(1+\gamma \theta)}\right] $
$ \Rightarrow \frac{50}{60}=\frac{1+\gamma \times 50}{1+\gamma \times 100} \Rightarrow \gamma=0.005 /{ }^{\circ} \mathrm{C}$

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