What are damped oscillations ? Obtain the differential equation for damped oscillations and write its possible solution. Explain with corresponding sketches, when there can be very heavy damping, critical damping and weak damping.
Write a short note on Holography.
Write a short note on Forced oscillations.
Write a short note on Applications of Bernoulli's equation.
Write a short note on Geostationary satellites.
Prove that the expression x^2+y^2+z^2-c^2t^2 is invariant under Lorentz transformation.
How do we infer the law of conservation of linear momentum from Newton's laws of motion? A stationary bomb explodes and on explosion, it fragments into three parts. Two of these part which are of equal masses fly apart perpendicular to each other with a velocity of 60 m/s each. The third part has a mass four times the other two. Find the magnitude and the direction of the velocity of the third part.
Discuss the Reynolds number for describing the stability of fluid flow, Air streams horizontally across an aeroplane wing of area 4\text{ m}^2 and weighing 300 kg. The air speed is 60 m/s and 40 m/s over the top surface and under the bottom surface respectively. Find (i) the lift on the wing and (ii) the net force on it, given that the density of air is equal to 1.293\text{ kg/m}^3.
Starting from the definition of angular momentum of a single particle, obtain an expression for the angular momentum of a rotating rigid body. Hence, discuss the time derivative of the angular momentum and deduce the law of conservation of momentum.
Explain the precession of a spinning top and show that precssional angular velocity is independent of the angle of inclination. A top is spinning with 20 rev/s about an axis inclined at 30^\circ with the vertical. Its radius of gyration is 5 cm. The centre of mass is \pi cm from the pivot point. Calculate the frequency of precession.
Distinguish between elastic and inelastic collision. Find the minimum distance an \alpha-particle with kinetic energy of 0.4 Mev can approach a stationary but free Lithium nucleus in a head-on collision.
Consider the motion of a rocket in a gravitational field and derive an expression for its final velocity when the fuel burns at a constant rate till it is fully consumed.
Describe the set-up of Michelson-Morley experiment. Why was a fringe shift expected in it? How are its negative results understood?
Simplify the following logic function and draw the corresponding logic diagram:- Y = (A+B).(A + C).(B+C)
Distinguish qualitatively between dia-, para-, ferro-, antiferro- and ferrimagnetism. How is the weak and temperature independence paramagnetism of metals explain?
If E_0 is the peak value of the input voltage V_{in} calculate the output voltage V_{out}.
Explain the working N-P-N transistor. Derive expression for the current and voltage gains.
What is the photovoltaic mode of operation for a photo-diode? Describe the construction and working of a silicon solar cell.
What is the basis of thermonuclear fusion? Estimate the order of temperatures required for promoting the fusion reaction of lighter nuclei. Calculate the Q-value of the proton-proton cycle. 4 {}_1^1 H \rightarrow {}_2^4 He + 2 {}_{+1}^0 e + Q.
In nature, we have basically four kinds of forces in the following order of increasing interaction strength: (i) Gravitational (ii) Weak (iii) electromagnetic (iv) Nuclear or strong Comment on their spatial dependence and give their strength in terms of dimensionless coupling constants.
