Properties of Matter 4 Question 3
5. The pressure that has to be applied to the ends of a steel wire of length $10 cm$ to keep its length constant when its temperature is raised by $100^{\circ} C$ is (For steel, Young’s modulus is $2 \times 10^{11} Nm^{-2}$ and coefficient of thermal expansion is $1.1 \times 10^{-5} K^{-1}$ )
(2014 Main)
(a) $2.2 \times 10^{8} Pa$
(b) $2.2 \times 10^{9} Pa$
(c) $2.2 \times 10^{7} Pa$
(d) $2.2 \times 10^{6} Pa$
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Answer:
Correct Answer: 5. (*)
Solution:
- The bubble will detach if,
$\int \sin \theta T \times d l=T(2 \pi r) \sin \theta$
Buoyant force $\geq$ Surface tension force
$$ \begin{aligned} \frac{4}{3} \pi R^{3} \rho _w g & \geq \int T \times d l \sin \theta \\ \left(\rho _w\right)\left(\frac{4}{3} \pi R^{3}\right) g & \geq(T)(2 \pi r) \sin \theta \\ \sin \theta & =\frac{r}{R} \end{aligned} $$
Solving, $\quad r=\sqrt{\frac{2 \rho _w R^{4} g}{3 T}}=R^{2} \sqrt{\frac{2 \rho _w g}{3 T}}$
No option matches with the correct answer.
