Experiments with Wires, Liquids, Heat and Sound: Quick Revision

A brief note on Experiments with Wires, Liquids, Heat and Sound. Read it before a practical examination. Try each question at the end before you open its answer.

Wires and liquids

• Young's modulus (Searle): $Y = \dfrac{4MgL}{\pi d^2\,\Delta L}$. The graph of $\Delta L$ against $M$ is a straight line through the origin. $Y = \dfrac{4gL}{\pi d^2 \times \text{slope}}$. Steel: $2.0 \times 10^{11}\ \text{N/m}^2$.
• Two wires: the reference wire cancels temperature and a sagging support. Load and unload, and take the mean.
• Surface tension: $T = \dfrac{r h \rho g}{2\cos\theta}$. The graph of $h$ against $1/r$ is a line through the origin with the slope $\dfrac{2T}{\rho g}$. Water at $20$ °C: $0.0728$ N/m.
• Viscosity: $\eta = \dfrac{2r^2(\rho - \sigma)g}{9v_t}$. The terminal speed is in proportion to $r^2$. Stokes' law needs $Re < 1$.

Heat and sound

• Mixtures: $m_s c_s(\theta_1 - T)$ $= (m_l c_l + m_c c_c)(T - \theta_0)$. Do not forget the calorimeter.
• Newton's law: $\theta - \theta_s = (\theta_0 - \theta_s)e^{-kt}$. A graph of $\ln(\theta - \theta_s)$ against $t$ is a line of slope $-k$.
• Resonance tube: $v = 2f(L_2 - L_1)$ and $e = \dfrac{L_2 - 3L_1}{2} \approx 0.6r$. In air $v \approx 331.3 + 0.606\,t$ m/s.

A worked example

A fork of $426$ Hz gives resonances at $19.4$ cm and $59.9$ cm. Find the speed of sound and the end correction.

1. The speed. $v = 2f(L_2 - L_1)$ $= 2 \times 426\ \text{Hz} \times 0.405\ \text{m}$ $= 345\ \text{m/s}$.
2. The end correction. $e = \dfrac{59.9 - 3 \times 19.4}{2}\ \text{cm}$ $= 0.85$ cm.

Practise with new numbers

Check yourself

1. A wire is stretched by $1.2$ mm under a load. If the same load acts on a wire of the same material and length but twice the diameter, what is the extension?

2. In a mixture experiment, $0.10$ kg of a hot metal is dropped into cold water. Why is the highest temperature read, and not the temperature after a long time?

3. The excess of temperature of a cooling liquid is $40$ K and falls to $20$ K in $12$ minutes. What is $k$?

Sources

• NCERT, Laboratory Manual: Physics, Class XI.
• NCERT, Physics Class XI, Chapters 8, 9, 10 and 14.
• OpenStax University Physics Volume 1, Chapters 12, 14 and 17.