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Physics Question on thermal properties of matter

A vertical column 50 cm long at 50∘^{\circ}C balances another column of same liquid 60 cm long at 100∘^{\circ}C. The coefficient of absolute expansion of the liquid is

A

0.005/∘C0.005 / ^{\circ} C

B

0.0005/∘C0.0005/^{\circ}C

C

0.002/∘C0.002/ ^{\circ}C

D

0.0002/∘C0.0002 / ^{\circ}C

Answer

0.005/∘C0.005 / ^{\circ} C

Explanation

Solution

     h1h2=ρ2ρ1=(1+γθ1)(1+γθ2)          [∵ ρ=ρ0(1+γθ)] \, \, \, \, \, \frac{h_1}{h_2}=\frac{\rho_2}{\rho_1} =\frac{(1+\gamma \theta_1)}{(1+\gamma\theta_2)} \, \, \, \, \, \, \, \, \, \, \bigg[ \because \, \rho =\frac{\rho_0}{(1+\gamma \theta)}\bigg] ⇒    5060=1+γ×501+γ×100⇒ 0.005/∘C\Rightarrow \, \, \, \, \frac{50}{60}=\frac{1+ \gamma \times 50}{1+\gamma \times 100} \Rightarrow \, 0.005 / ^{\circ}C