1. A ball of density d is dropped on to a horizontal solid surface. It bounces elastically from the surface and returns to its original position in time t1. Next, the ball is released and it falls through the same height before striking the surface of a liquid of density dL. What is the expression for the time t2 the ball takes to come back to the position from which it was released in terms of d, t1 and dL. d is less than dL.
2. A straight segment of a circuit with length L is carrying a current I (in the positive direction of x). It is placed between two infinitely long conductors in which current I is flowing in opposite directions are placed perpendicular to it. What is the expression for th force acting on the circuit segment?
3. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fasted photoelectrons emitted from sodium is 0.73 eV. The work function for sodium is 1.82 eV. Find the energy of the photons causing the photoelectric emission.
4. A charge of Q is uniformly distributed over a spherical volume of radius R. What is the expression for the energy of the system?
5. Light is incident at an angle α on one planar end of a trasparent cylindrical rod of refractive index n. Determine the least value of n so that the light enteriing the rod does not emerge from the curved surface of the rod irrespective of the value of α.
(Source: 1992 JEE paper)