Q140 / 160 · TS EAMCET 2011 · Physics
A non-conducting body floats in a liquid at $20^{\circ} \mathrm{C}$ with $\frac{2}{3}$ of its volume immersed in the liquid. When liquid temperature is increased to $100^{\circ} \mathrm{C}, \frac{3}{4}$ of body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of container of the liquid)
- Correct answerA$15.6 \times 10^{-4 \circ} \mathrm{C}^{-1}$
- B$156 \times 10^{-4 \circ} \mathrm{C}^{-1}$
- C$1.56 \times 10^{-4 \circ} \mathrm{C}^{-1}$
- D$0.156 \times 10^{4 \circ} \mathrm{C}^{-1}$
Solution
Coefficient of real expansion
$\begin{aligned}
& \gamma_R=\frac{V_2-V_1}{V_1\left(t_2-t_1\right)} \\
& \text { Here, } \quad V_2=\frac{3}{4}, V_1=\frac{2}{3} \\
& \text { and } \quad\left(t_2-t_1\right)=(100-20)=80^{\circ} \mathrm{C} \\
& \therefore \quad \gamma_R=\frac{\left(\frac{3}{4}-\frac{2}{3}\right)}{\frac{2}{3}(80)}=\frac{1}{640} \\
& =15.6 \times 10^{-4} \circ \mathrm{C}^{-1} \\
&
\end{aligned}$
Hence, the correct answer is option: 'A'.