Assignment 1

BABU BANARASI DAS NATIONAL INSTITUTE OF TECHNOLOGY & MANAGEMENT, LUCKNOW DEPARTMENT OF PHYSICS B.Tech. 1st year ASSIGNMENT- 1 (RELATIVISTIC MECHANICS) 1. Prove that a frame moving with constant speed along the positive x-direction relative to an inertial frame will also be inertial. 2. A ball has velocity (4i – 5j +10k) m/s relative to the train moving with velocity (3i + 4j) m/s relative to an observer in ground. Calculate the velocity of the ball relative to the ground. 3. Using the concept of Lorentz Fitzgerald contraction. Show that in Michelson Morley experiment t1=t2 4. In Michelson Morley experiment the distance of mirrors from the glass plate is 11 m and the orbital velocity of earth is 3X104 m/s. The wavelength of light used is 5500Å. Calculate the fringe-shift of fringe pattern. (Given c=3X108 m/s) 5. Show that from Lorentz transformation that events simultaneous (t1=t2) at different positions (x1≠x2) in the reference frame S are not in general simultaneous in another reference frames S’. 6. In an inertial frame S, a red light and a blue light are separated by a distance ∆x=2.45km. with the red light at the larger value of x. The blue light flashes and 5.35 μs later the red light flashes. Frame S’ is moving in the direction of increasing x with speed v = 0.855c. What is the distance between two flashes and the time between them as measured in S? 7. A cube of volume V0 and density ρ0 with respect to frame S is placed on x-axis of the frame. Frame S’ is moving with constant velocity v along positive x- direction relative to a stationary frame S. Show that the volume and density of this cube will be V= (V0 / γ ) & ρ = ρ0 γ2 where γ = 1/√(1- v2/c2) 8. Prove that the rest mass of photon is zero. 9. Calculate the percentage contraction of a rod moving with velocity 0.8c m/s in a direction inclined at 60° its own length. 10. A train of length 150m when passes through a tunnel of length 125m with velocity of 2.4x 108 m/s towards the tunnel (i) find the length of