The speeds v of waves on the surface of a liquid is given by v = \sqrt{\frac{TK}{P} + \frac{g}{k}} where T is the surface tension of the liquid of density P > K = 2\pi / \lambda, \lambda being the wavelength of the wave and g is acceleration due to gravity Find the wavelength and frequency of waves on water which move with minimum speed.
Write a note on Oscillations with two degrees of freedom.
Monochromatic light of wavelength due to diffraction, and critically; comment on [Source text is incomplete in the available scan.]
Derive an expression for the resolving power of a diffraction grating.
A muon (\mu meson) is for med high up in the atmosphere and travels towards the earth with a speed of 0.992\text{ c}. It decays af ter travelling a distance of 6.0\text{ km}. In what time does the muon decay as measured (i) by us and (ii) in its own frame of reference? What is the distance covered the muon in its own frame of reference?
Show that the kinetic energy T of relativistic particle moving with momentum p is T = P^2 / m + m_0 What m_0 its rest mass and m is its relativistic mass.
Write a note on Predictions of general theory of relativity and their experimental verification.
Write a note on Coriolis force and its manifestations.
A steel ball 1.00\text{ mm} in diameter falls at a constant speed of 0.176\text{ cm s}^{-1} in a large vessel filled with oil. Calculate the dynamic viscosity of the oil (Density of steel = 7,700\text{ kg/m}^3 density of oil = 900\text{ kg/m}^3).
Find the expression for the rise of a liquid between two parallel plates separated by a distance t and dipped vertically in the liquid.
Air is blown through a pipe AB, at a rate of 15\text{ litres per minute}. The area of cross-section at A is 2\text{ cm}^2 whereas at B it is 0.2\text{ cm}^2. A tube abc, containing some water, is connected as shown. Find the difference in height, \Delta h, between the levels of water in the tube abc.
For an isotropic solid define Young's modulus of elasticity Y, coefficient of rigidity \eta and Poisson's ratio \alpha. Establish the relation. \sigma = \frac{Y - 2\eta}{2\eta}
Find the linear acceleration of the center of gravity of a uniform disc which rolls down an inclined plane without slipping. The angle of inclination is 30^\circ.
The mean distance of the Earth from the Sun is 1.496 \times 10^{11}\text{ m}, while that of Saturn is 1.427 \times 10^{12}\text{ m}. Find the time taken by Saturn to complete one revolution round the Sun.
Draw a complete circuit for common emitter (small signal) amplifier for low frequencies and explain briefly its working.
Give an account of the basic principles of radio transmission and reception. Detailed circuits are not necessary but schematic diagrams indicating functions of various units may be shown.
Explain, on the basis of bond structure, the behaviour of insulators and conductors. Describe the effect of adding donor or acceptor impurities on conduction in a semi-conductor. Explain the action of a p-n junction as a rectifier. \begin{aligned} \text{Mass of electron} &= 9.1 \times 10^{-31}\text{ kg} \\\\ 1\text{ a.m.u} &= 931\text{ MeV} \\\\ \text{Avogadro's numbers} &= 6.1 \times 10^{23}\text{ (gm-mole)}^{-1} \\\\ \varepsilon_0 &= 1/36\pi \times 10^{-9}\text{ f/m} \\\\ h &= 6.6 \times 10^{-27}\text{ erg sec} \\\\ c &= 3.0 \times 10^{10}\text{ cm/sec} \\\\ 1\text{ eV} &= 1.6 \times 10^{-19}\text{ erg} \\\\ &= 1.6 \times 10^{-19}\text{ joule} \end{aligned}
A triode has a transconductance (g_m) of 1,600\text{ micromhos}. The following table gives two sets of the plate voltage (E_b), the grid voltage (E_c) and the plate current (I_b).
| E_b | E_c | I_b |
| 250\text{ V} | -22\text{ V} | 12.6\text{ mA} |
| 180 | -16.5 | 12.0 |
Define the terms amplification factor and plate resistance and calculate them for the above case.
Distinguish between dia-, para- and ferromagnetism. Give an account of Weiss theory of ferromagnetism.
Which of the following reactions are forbidden and why? \begin{aligned} p &\longrightarrow n + e^+ + u_e \\\\ \pi^+ &\longrightarrow \mu^+ + u_\mu \\\\ \text{H}^2 &\longrightarrow \text{He}^3 + e^- + e \end{aligned}
