A solid cylinder released from rest rolls (without slipping) downs piano of length l inclined at angle \theta with the horizontal. Deduce an expression for the velocity of the centre of mass of the cylinder at the bottom of the plane, neglecting friction.
State Bernoulli's theorem for an ideal liquid. Deduce the related equation from first principles and describe one application in relation to sonic measurement technique or device.
The spike heel on a girl's shoe is a square, 1.0 cm on an edge. If her mass is 50kg, calculate (in atmospheres) the pressure exerted on the ground when she balances on one heel.
A spinning top shows precession. Explain how the precession rate changes as the spinning becomes slower and as the inclination of the spinning axis from the vertical increases.
What is the angular momentum of an earth satellite of mass 100 kg which moves in a circular orbit of radius equal to twice the radius of the earth? Derive the relation used.
The mass of a molecule of DNA from T2 bacteriophage is 1.2 \times 10^8\text{ a.m.u.} The molecule is a double helix of 1.2 \times 10^4 turns and the radius of gyration of the helix is 6.7\text{ \AA}. If the rotational energy of the molecule about the axis of the helix is equal to thermal energy at 300 K, deduce the value of \omega, the angular frequency of rotation.
A girl on skis (mass 60kg including skis) reaches the bottom of a hill going 20\text{ ms}^{-1}. What is her momentum? She then strikes a snowdrift which slops her on 3s. What average force does the snow exert on the girl? Assuming that the force remains constant. How far does the girl penetrate the snowdrift?
State how Rutherford's experiments on alpha scattering by thin gold foils established that
(i) the positive charge in an atom is confined to a nucleus of radius far less than the atomic radii, and
(ii) the Coulomb law is valid down to such small distances. Why do the electrons not participate in the interactions appreciably?
What is a P.N. junction? Describe with energy level diagram the formation of double layer of charges which generates a potential difference (V) across, the junction. Hence show that the capacitance of the double layer. C=KV^{-1/2}, where K is a constant. State some practical use of this relation between C and V.
Discuss briefly the three types of interaction between elementary particles, and explain the relative strength of the various kinds of interaction between elementary particles.
What is alpha decay? Deduce an expression for the potential barrier penetrability for alpha particle in a nucleus. Show how the penetrability is related to the alpha decay constant.
What is deuterium? Is deuterium the same as hydrogen? Hon can you obtain deuteron from deuterium? Calculate the frequency of the oscillating potential applied to a cyclotron as to accelerate deuterons when the magnetic induction has a constant value of 2.5\text{ Wb/m}^{2}.
State and explain Pauli's exclusion principle. Estimate the total number of electron states in a many electron atom for a given principal quantum number n.
Discuss the origin of line spectrum and continuous spectrum of X-rays. What is Duance and Hunt limit for X-ray spectrum? Can you obtain the value of 'h' (Planck's const.) precisely from a knowledge of the Duane and Hunt limit. An X-ray tube is operated it 20\text{ kV}. Determine the wavelength limit of continuous X-rays.
An electron moves with a speed of 10^{3}\text{ m/sec}, accurate to 0.008\%. Find the accuracy with which the position of the electron can be located.
Derive Schrodinger equation for a linear harmonic oscillator, and determine its eigenvalue and eigenfunctions. Discuss the significance zero point energy.
State and explain Einstein's photoelectric emission equation, Distinguish between extrinsic and intrinsic photo electric effects. What is "quantum field"? On what factors does the quantum yield depend?
Calculate the mean free path of helium atoms at NTP, the coefficient of viscosity being 190 \times 10^{-7}\text{ kg m}^{-1}\text{ s}^{-1}. 1\text{ atmospheric pressure} = 0.076 \times 136 \times 10^3 \times 9.81\text{ Nm}^{-2}.
A Carnot’s engine is made to work between 0^\circ\text{C} and -200^\circ\text{C}. Calculate us efficiency. Derive the expression you use of calculation.
Write a short note on Production of low temperature using adiabatic demagnetisation.
