GALGOTIAS COLLEGE OF ENGINEERING & TECHNOLOGY
Question bank ENGINEERING PHYSICS – I RAS -101 (SEMESTER-I)
B.Tech. (ALL BRANCHES) AS PER AKTU SYLLABUS (w.e.f 2016)
PHYSICS_FACULTY DEPT. OF APPLIED SCIENCE AND HUMANITIES GCET , GR.NOIDA SESSION : 2016-17
1. Differentiate between inertial and non-inertial frames of reference. Explain each with suitable example. 2. Is the earth an inertial frame? Explain. 3. What was the objective of Michelson-Morley experiment? 4. Write the Lorentz transformation equations for position and time. Show that under special case it reduces to Galilean transformation equations. 5. State the postulates of the Special Theory of Relativity. 6. Write the Lorentz Transformations equations if an observer O′ is moving with uniform speed v with respect to another observer O along negative z-axis. 7. Define proper length. Briefly explain what you mean by length contraction. 8. What is time dilation? Give an example to show that the time dilation is a real effect? 9. Show that the rest mass of photon is zero. 10. What is the significance of Einstein’s mass energy relation? NUMERICAL PROBLEMS 1. An event occurs at x=100m, y=5m, z=1m and t=1x10-4sec in a frame S. Find the coordinates of this event in a frame S’ which is moving with velocity 2.7x108 m/sec with respect to the frame S along the common XX’ axis using Lorentz transformation. (Ans. x’=-6.17x10-4 m, y’=5m, z’=1m, t’=2.287x10-4 sec) 2. A cube has a proper volume of 1000 m3. Find the volume as determined by an observer O’ who is moving with a velocity of 0.8c relative to the cube in a direction parallel to one edge.
(Ans. 600 m3)
3. Calculate the length and orientation of a meter rod in a frame of reference moving with a uniform velocity equal to 0.8c, in a direction making an angle of 30 ̊with the rod.
(Ans. 0.72 m, 43.90)
4. A circular lamina moves with its plane parallel to the X-Y plane of a reference frame S at rest. Assuming its motion to be along x-axis, calculate the velocity, at which its surface area would appear to be reduced to half to an observer in frame at rest. (Ans. 2.6x108 m/sec) 5. The mean life of µ-mesonsis 2x10-6 s. Calculate the mean life of the mesonswhen moving with a velocity of 0.998c.
(Ans. 31.7x10-6 sec)
6. The lifetime of π+-meson is 2.5x10-8 sec in its own frame of reference. If a beam of these mesons of velocity 2.4x108 m/s is produced, calculate the distance, the beam can travel before the flux of meson is reduced to 1/e times the initial value. (Ans. 10m) 7. A clock showing correct time when at rest, losses one hour in a day when it is moving. What is its velocity?
(Ans. 0.286c)
8. Two particles are approaching towards each other with the speed of light. What is (Ans. 3x108 m/sec)
their relative velocity?
9. A particle has a velocity ’=3i + 4j +12k meter/sec in a co-ordinate system moving with velocity 0.8c relative to laboratory along +vedirection of x-axis. Find laboratory frame.
in a
(Ans. =2.4x108i + 2.4j + 7.2k m/sec)
10. On earth’s surface, mass of a man is 100 kg. When he is in rocket moving with a speed of 4.2x107 m/sec relative to the earth, what is his mass observed by (i) observer on earth, and (ii) observer on rocket.
(Ans. (i) 101kg and (ii) 100kg)
11. A person observes two men, each of rest mass 60 kg, moving towards each other, each with a velocity of 0.5 c. What is the mass of one man as observed by the other? (Ans. 100 kg) 12. How fast an electron move in order that its mass equals the rest mass of the proton? (Ans. 2.99x108 m/sec) 13. Find out the velocity of a particle if its kinetic energy is three times the rest mass energy.
(Ans. 2.9x108 m/sec)
14. Calculate the amount of work to be done to increase the speed of electron from 0.6c to 0.8c. Given that the rest energy of an electron is 0.5 MeV.
(Ans. 3.36x10-14 joule)
15. A photon in the S-frame is moving in the x-y plane such that its direction of motion makes an angle of θ with the x-axis. Calculate its speed in the S′ frame which moves with a constant velocity v with respect to the S-frame and along the x-axis of the Sframe.
(Ans. c)
LONG ANSWER TYPE QUESTIONS 1. What was the objective of Michelson-Morley experiment? Explain the obtained result and the conclusion that can be drawn from it. How are the negative results explained? 2. Describe the Michelson-Morley experiment and explain the physical significance of negative results. 3. Discuss the Galilean transformation for position, velocity and acceleration.