# [Free] IIT JAM Physics Test Series 2023 : Modern Physics – (Special Theory of Relativity)

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Now In this particular Post of IIT JAM Physics Test Series, you will get a test of the topic Special Theory of Relativity of Chapter Modern Physics. There are total 15 Questions given below also Answers are attached at the end of the test so that you can verify your answers after completing the test. So, Practice these Questions and Do your Best. Also Solve IIT JAM Physics Previous Year Question Paper. And Don’t Forget to Share with Your Friends.

## [Free] IIT JAM Physics Test Series 2023 : Modern Physics – (Special Theory of Relativity)

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 ×1012 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 (x1, t1) and (x2, t2) . In frame O’, these occur simultaneously . The value of (x2 – x1)/(t2 – t1) 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 v0 be the speed at which the kinetic energy equals the rest mass energy of the particle. Then

• (A) v0 = c/√2
• (B) v0 = √3c/
• (C) v0 = c
• (D) v0 > 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 106 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 ×108 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

Hope you like the test given above for IIT JAM Physics 2023 of Topic – Special Theory of Relativity of the Chapter Modern Physics. To get more Information about any exam, Previous Question Papers , Study Material, Book PDF, Notes etc for free, do share the post with your friends and Follow and Join us on other Platforms links are given below to get more interesting information, materials like this.

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

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