Consider a light beam passing through a horizontal column of water moving with a velocity 'v'. Determine the speed u of the light measured in the lab frame when the beam travels in the same direction as the flow of the water. (Speed of water = v (lab frame), and refractive index = n)
A particle moves in an elliptical orbit in an inverse-square-law central force field. If the ratio of the maximum angular velocity to the minimum angular velocity of the particle in the orbit is n, then show that the eccentricity of the orbit is \varepsilon = \frac{\sqrt{n} - 1}{\sqrt{n} + 1}.
A mouse of mass m jumps on the outside edge of a freely turning ceiling fan of rotational inertia I and radius R. By what ratio does the angular velocity change ?
A three-particle system consists of masses \text{m}_i,\ i = 1, 2, 3 and their respective coordinates (\text{x}_i, \text{y}_i, \text{z}_i) : m_1 = 3m,\ (x_1, y_1, z_1) = (a, 0, a), m_2 = 4m,\ (x_2, y_2, z_2) = (a, a, -a), m_3 = 2m,\ (x_3, y_3, z_3) = (-a, a, 0), where m and a are positive constants. Calculate the inertia tensor of the system.
A particle of mass m rests on a smooth plane. The plane is then raised to an inclination angle \theta at a constant rate \alpha (\theta = 0 at t = 0), causing the particle to move down the plane, as shown in the figure below.
Write down the Lagrangian and determine the equations of motion. Solve the resulting equation for "r" to obtain the expression for r(t).
A pair of transistors operates in a class B push-pull circuit with a power supply of voltage V_{\text{cc}} = 12\text{ V}. If the turns ratio of the output transformer is 2 and the load resistance R_{\text{L}} is 6\ \Omega, calculate the maximum output power and maximum dc power supplied. Hence find efficiency of the circuit. Neglect transformer winding resistance.
Find the output voltage of the three-input adder circuit shown below.
Draw the circuit of a phase shift oscillator using transistor. Obtain the expression for the frequency of oscillations and condition for sustained oscillations. Give necessary equivalent circuit while deriving the expression of frequency of oscillations and condition for sustained oscillations.
Estimate the current gain of an n-p-n transistor if only 0\cdot 3\% of the conduction electrons that enter the base from the emitter recombine in the base region.
A small magnet is placed on the surface of a disc of normal material. Explain what happens when the disc is cooled down so that it becomes superconducting. Can this be explained from classical viewpoint if we simply treat the superconductor as a material which has zero resistivity ?
Derive the expression for electron concentration in the conduction band of an intrinsic semiconductor.
Explain drift velocity, mobility and conductivity of an intrinsic semiconductor.
Calculate the total conductivity in an intrinsic semiconductor. How does this conductivity change with temperature ?
What do you mean by nuclear reactors ? With a neat diagram, describe the essential parts of a nuclear reactor and discuss about its applications.
An atomic power reactor can deliver 300\text{ MW}. If due to fission of each atom of {}_{92}\text{U}^{235}, the energy released is 200\text{ MeV}, calculate the mass of uranium fissioned per hour.
What is the source of the Sun's energy ? Explain with proper nuclear reaction.
Draw the baryon octet according to Murray Gell-Mann.
The nuclear radius of {}_8\text{O}^{16} is 3 fermi. What will be the nuclear radius of \text{U}^{235} ?
The most intense vibrational bands of CO and HCl molecules have the wave numbers 2\cdot 143 \times 10^5\text{ m}^{-1} and 2\cdot 886 \times 10^5\text{ m}^{-1} respectively. Calculate the force constants of these molecules.
In an atomic physics experiment a beam of p-state atoms is passed through a non-uniform magnetic field. After passing through the magnetic field the atomic beam strikes at the screen and is detected as shown in the given figure. Obtain an expression of the force acting on the p-atoms beam due to gradient in the magnetic field acting along z-axis as shown. Also comment on the number of spots that are found on the screen as an outcome and explain.
