A uniform rope of mass M and length L is hanging from a rigid support. A transverse wave travels along the rope. Calculate the speed of the wave at a distance x from the free end the time taken by the wave to travel the whole length.
The amplitude of damped oscillator of frequency 300\text{ Hz} reduces one-tenth of its initial amplitude after 3000 oscillations. Calculate the damping constant and the time in which its energy will reduce to one-tenth of its initial energy.
In a hydrogen atom for the 2\text{p} \to 1\text{ s} transition the probability per unit time is 6 \times 10^8\text{ s}^{-1}. Calculate the angular frequency of the emitted photons and the order of Einstein's coefficient \text{B}_{21}.
Write a short note on Coriolis force and its effects.
Moving in a closed elliptical orbit, Halley's comet goes round the Sun once every 75 years. At its point of closest approach its distance from the Sun is 8.9 \times 10^7\text{ km}. If mass of the Sun is 2 \times 10^{30}\text{ kg}, what will be the greatest distance of the comet from the Sun ?
In the ammonia molecule the three hydrogen atoms form an equilateral triangle. The distance between the centre of this triangle from each hydrogen atom is 0.939\text{ \AA}. The nitrogen atom is at the apex of the pyramid with the three hydrogen atoms forming the base. The distance between the hydrogen and nitrogen atoms is 1.014\text{ \AA}. Find the position of the centre of mass relative to the nitrogen atom.
The tides in oceans on Earth are produced by gravitational pull of the Sun and the Moon. The pull due to Sun is much greater than the pull due to Moon. Explain, why tides due to Sun are only about 0.4 times as high as that due to Moon. The mass of the Sun is 2 \times 10^7 times the mass of the Moon and the distance between Sun and Earth is 400 times the distance between Moon and Earth. The radius of the Earth is 6.4 \times 10^6\text{ m}.
Write a short note on Motion of rocket.
A particle is moving under a central force field. Obtain the equations of motion and prove that in such a field the areal velocity of the particle remains constant.
Obtain the relativistic transformation relation for density in inertial frames. Why is the equivalent energy corresponding to 1 amu of mass?
Distinguish between streamline and turbulent motion. Define Reynolds number. When a sphere of radius 1.2\text{ mm} moves in glycerine, the laminar flow observed if the velocity of sphere does not exceed 0.23\text{ ms}^{-1}. At that minimum velocity of sphere of radius 5.5\text{ cm} will the flow in water become turbulent? The viscosities of glycerine and water are 11.9\text{ P} and 0.011\text{ P} respectively. The density of glycerine is 1.2 \times 10^{-3}\text{ Kg/m}^3.
Explain processional motion of a top. A solid sphere of radius 2\text{ cm} and mass 50\text{ gm} has a thin nail of length 5\text{ mm} fixed perpendicular to its surface. When this sphere spins like a top with a speed of 20 rev./second what will be its processional speed?
Define ex-OR. Give its truth table and draw the possible logic blocks.
Derive the expression for the frequency spectrum of a carrier wave of frequency f_c which is amplitude modulated by a frequency f_m. A certain transmitted radiates 9\text{ kW} of power when the carrier wave is unmodulated and 10.12\text{ kW} power when the carrier wave is sinusoidally modulated. Calculate the modulation index.
A Si BJT is connected as shown Fig . Show that it is in active region and works as an amplifier Calculate its mid frequency gain, given that BJT has h_{ie} = 1\text{ k}\Omega, h_{oe} = h_{re} = 0, I_{co} = 20\text{ nA}.
Write a comparative account of the following four processes: (i) \beta - decay (ii) positron emission (iii) electron capture (iv) inverse \beta- decay
Define parity for a quantum mechanical system. Describe an appropriate experiment proving the parity violation in weak interaction. How can the parity violation in weak interaction be understood ? Explain.
Taking only the spin motion of electron, proton and neutron and assuming them as point particles, obtain their magnetic moments. How far the values thus obtained agree with experimental values? If not, why? Explain.
Calculate the bond length and force constant of the bond of {}^{12}\text{C}\ {}^{16}\text{O} molecule; given 0 \rightarrow 1 rotational line in v = 0 state is at 115.3\text{ GHz} and the wavelength of the vibrational frequency is 14.7\ \mu\text{m}.
Write a short note on Stellar spectra.
