aberration and Doppler effect, mass-energy relation, simple applications to a decay process; Four dimensional momentum vector; Covariance of equations of physics. Questions: Q 1. A meson of rest mass π\piπ comes to rest and disintegrates into a muon of rest mass μ\muμ and a neutrino of zero rest mass. Show that the kinetic energy of …
Michelson-Morley experiment and its implications; Lorentz transformations-length contraction, time dilation, addition of relativistic velocities, Questions: Q 1. Two β-particles A and B emitted by a radioactive source R travel in opposite directions, each with a velocity of 0.9 c with respect to the source. Find the velocity of B with respect to A (Here c …
Elasticity, Hooke’s law and elastic constants of isotropic solids and their inter-relation; Questions: Q 1. State and explain stokes’ law. A drop of water of radius 0.01 m is falling through a medium whose density is 1.21kg/m31.21 kg/m^31.21kg/m3 and η=1.8×10−5N−s/m\eta= 1.8\times 10^{-5}N-s/mη=1.8×10−5N−s/m . Find the terminal velocity of the drop of water. [15 marks] …
Elasticity, Hooke’s law and elastic constants of isotropic solids and their inter-relation; Questions: Q 1. A rubber cord 1mm in diameter and 1 m long is fixed at one end and a weight of 1 kg is attached to the other end. If they Young’s modulus of rubber is 0.05×1011cm−20.05 × 10^{11} cm^{-2}0.05×1011cm−2, then find …
Equation of motion for rotation; Molecular rotations (as rigid bodies); Di and tri-atomic molecules; Precessional motion; top, gyroscope. Questions: Q 1. A sphere of mass 0.5kg rolls on a smooth surface without slipping with a constant velocity of 3.0 m/s. Calculate its kinetic energy (2021) Q 2. Where do you find the applications of gyroscope? …
Rigid body; Degrees of freedom, Euler’s theorem, angular velocity, angular momentum, moments of inertia, theorems of parallel and perpendicular axes, Questions: Q 1. A homogeneous right triangular pyramid wih the base side aaa and height 32a\frac32a23a is shown below. Obtain the moment of inertia tensor of the pyramid. [15 marks] Q 2. The angular momentum …
Gravitational field and potential due to spherical bodies, Gauss and Poisson equations, gravitational self-energy; Two-body problem; Reduced mass; Questions: Q 1. Two bodies of masses and are placed at a distance d apart. Show that at this position where the gravitational field due to them is zero, the potential is given by V=−Gd(M1+M2+M1M2)V= – \frac …
centripetal and Coriolis accelerations; Motion under a central force; Conservation of angular momentum, Questions: Q 1. For a freely falling body from the height ‘h’ on the surface of the earth in the northern hemisphere with a latitude ‘θ’, show that the deviation of the body towards the east at the final stage is given …
System of particles; Centre of mass, Elastic and inelastic collisions; Rutherford scattering; Centre of mass and laboratory reference frames. Questions: Q 1. Find the laboratory differential cross-section area for the scattering of identical particle of charge e and mass m, if the incident velocity is v. (15 marks) Q 2. Determine the location of the …
Laws of motion; conservation of energy and momentum, Conservation theorems for energy, momentum and angular momentum; Questions: Q 1. A body of mass m splits into two masses m1m_1m1 and m2m_2m2 by an explosion. After the split, the bodies move with a total kinetic energy of TTT in opposite direction. Show that their relative speed …
