Practice Questions on the Special Theory of Relativity with Answers

**Questions on Special Theory of Relativity with Answers**

**Q1. In an inertial frame S, a stationary rod makes an angle θ with the x-axis. Another inertial frame S’ moves with a velocity ‘v’ with respect to S along the common x-x’ axis. As observed from S’ the angle made by the rod with the x’- axis is θ’. Which of the following statements is correct ?**

- (A) θ’ < θ
- (B) θ’ > θ
- (C) θ’ θ if v is positive
- (D) θ’ > θ iv is negative and θ’ < θ if v is positive.

**Q2. A space crew has a life support system that can last only for 1000 hours. What minimum speed would be required for safe travel of the crew between two space stations separated by a fixed distance of 1.08 ×10 ^{12} km ?**

- (A)
^{c}/_{√3 } - (B)
^{c}/_{√2} - (C)
^{c}/_{2} - (D)
^{c}/_{√5}

**Q3. Light takes 4 hours to cover the distance from Sun to Neptune. If you travel in a spaceship at a speed 0.99c (where ‘c’ is the speed of light in vacuum), the time (in minutes) required to cover the same distance measured with a clock on the spaceship will be approximately**

- (A) 34
- (B) 56
- (C) 85
- (D) 144

**Q4. A proton from outer space is moving towards earth with velocity 0.99c as measured in earth’s frame A spaceship, traveling parallel to the proton, measures proton’s velocity to be 0.97c. The approximate velocity of the spaceship, in the earth’s frame is**

- (A) 0.3c
- (B) 0.2c
- (C) 0.4c
- (D) 0.5c

**Q5. A collimated beam of pions originate from an accelerator and propagates in vacuum along a long straight beam pipe. The intensity of this beam was measured in the laboratory after a distance of 75 m and found to have dropped to one-fourth of its intensity at the point of origin. If the proper half-life of a pion is 1.77 x 10 ^{-8} s, the speed of the pions in the beam, as measured in the laboratory, must be**

- (A) 0.99c
- (B) 0.98
- (C) 0.97
- (D) 0.96

**Q6. In a certain inertial frame two light pulses are emitted at point 5 km apart and separated in time by 5 μs. At observer moving at a speed V along the line joining these points notes that the pulses are simultaneous. Therefore V is**

- (A) 0.7c
- (B) 0.8c
- (C) 0.3c
- (D) 0.9c

**Q7. A k meson (with a rest mass of 494 MeV) at rest decays into a muon (with a rest mass of 106 MeV) and; neutrino. The energy of the neutrino, which can be taken to be massless, is approximately**

- (A) 120 MeV
- (B) 236 MeV
- (C) 300 MeV
- (D) 388 MeV

**Q8. Two frames, O and O’, are in relative motion as shown. O’ is moving with speed ^{c}/_{2} , where c is the speed of light. In frame O, two separate events occur at (x_{1}, t_{1}) and (x_{2}, t_{2}) . In frame O’, these occur simultaneously . The value of (x_{2} – x_{1})/(t_{2} – t_{1}) is**

- (A)
^{c}/_{4} - (B)
^{c}/_{2} - (C) 2c
- (D) c

**Q9. Light takes approximately 8 minutes to travel from the Sun to the Earth. Suppose in the frame of the Sun an event occurs at t = 0 at the Sun and another event occurs on Earth at t =1 minute. The velocity of the inertial frame in which both these events are simultaneous is:**

- (A)
^{c}/_{8}with the velocity vector pointing from Earth to Sun - (B)
^{c}/_{8}with the velocity vector pointing from Sun to Earth - (C) The events can never be simultaneous – no such frame exist
- (D) c√[1- (
^{1}/_{8})^{2}] with velocity vector pointing ion Sun to Earth

**Q10. The kinetic energy of a free relativistic particle is me ?, where E and m are its total energy and rest mass respectively. Let v _{0} be the speed at which the kinetic energy equals the rest mass energy of the particle. Then**

- (A) v
_{0}=^{ c}/_{√2 } - (B) v
_{0}=^{√3c}/_{2 } - (C) v
_{0}= c - (D) v
_{0}> c (so this can never happen)

**Q11. A galaxy is receding relative to us at a speed of 3000 km/s. It emits hydrogen redline of wavelength 6560 Å. When seen by us, the wavelength of this radiation will appear to be**

- (A) higher by approximately 65 Å
- (B) lower by approximately 65 Å
- (C) lower by approximately 6 Å
- (D) higher by approximately 6 Å

**Q12. Muons of kinetic energy E are produced in collision with a target in a laboratory. The mass of a muon is 10 ^{6} MeV/c and its half-life is 1.4×10 s in its rest frame. What should be the minimum value of E if more than half the muons created at the target are to reach a detector 840 m away ?**

- (A) 106 MeV
- (B) 212 MeV
- (C) 130 MeV
- (D) 189 MeV

**Q13. A muon, whose life-time at rest is 2 x 10 ^{-6} sec, is travelling through the laboratory at three-fifth of the speed of light. It will last in**

- (A) 2 × 10
^{-6}sec - (B) 3.0 × 10
^{-6}sec - (C) 2.5 × 10
^{-6}sec - (D) 3.5 × 10
^{-6}sec

**Q14. Relative to a stationary observer, a rod of length 1.0 metre is moving at 0.8 times the speed of light in vacuum. It would appear to the observer that the rod’s length is :**

- (A) 0.8 m
- (B) 0.6 m
- (C) 1.0 m
- (D) 1.25 m

**Q15. A particle is moving at a speed of 2.6 ×10 ^{8} m/s relative to the laboratory. Its lifetime as measured by an observer in the laboratory is 4.7 × 10^{-6} s. The lifetime of the particle in its own rest frame is about**

- (A) 2.3 ×10 s
- (B) 9.4 ×10 s
- (C) 4.7 ×10 s
- (D) 14.4 ×10 s

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*Answer Key* (if you find any answer wrong, feel free to Correct us)

*Answer Key*

01. | (B) | 06. | (C) | 11. | (A) |

02. | (B) | 07. | (B) | 12. | (B) |

03. | (A) | 08. | (C) | 13. | (B) |

04. | (D) | 09. | (B) | 14. | (B) |

05. | (A) | 10. | (B) | 15. | (A) |