Section A
Q1. Two particles each of rest mass 1 gm collide head-on with the speed 0.8c to stick together at rest. Find the mass of the final composite. Calculate the effective gravitational acceleration at the equator due to the Earth's rotation. [R_earth = 6400 km] A 15.0 cm violin string, fixed at both the ends, is vibrating with the largest wavelength. The speed of the wave in this string is 250 m/s, and the speed of sound in air is 350 m/s. What is the frequency and wavelength of the emitted sound wave? Determine the position of focal points, principal points and nodal points for a spherical lens of radius 20 cm. The refractive index of the material of the lens is 3/2. Indicate the positions of all the points in a diagram. A parallel beam of sodium light of wavelength 5893 Å is incident on a diffraction grating. The angle between the first order spectra on either side of the normal is 27^{circ}42'. Find :
(i) The number of rulings/mm on the grating.
(ii) The greatest number of bright images obtained.