Suppose there is someone in a spaceship ̄O moving at some velocityνrelative to anobserver O. The person in the spaceship turns his stereo on and starts listening to some music.With a clock he measures the time interval between two beats ∆ ̄t = ̄tB- ̄tA. Prove that thetime interval measured by O is ∆t = ∆ ̄t/√1−ν2/c2.

Q: Show that the speed of an object having momentum of magnitude p and mass m is…

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Q: According to observer O, two events occur separated by a time interval At = +0.465 µs and at…

A: Given: Time interval ∆t=+0.465 μs Location separation ∆x=+53.4 m Speed : v = 0.762c

Q: An astronaut on a spaceship traveling at 0.75c relative toEarth measures his ship to be 23 m long.…

A: Given, Velocity, v=0.75 c, Length of ship, l=23 m, and Time measured on the ship, t=28 min.

Q: The control panel on a spaceship contains a light that blinks every 2.71 s as observed by an…

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Q: Two rockets are approaching each other on a collision course. Relative to a stationary observer on…

A: Given data: The lengths of rocket is L. The speed of rocket 1 is v1=9/10 c=0.9c. The speed of…

Q: The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6…

A: (a)The mean life time as measured by the observer on earth can be given as

Q: A cube has a volume of 1.2 cm and a mass of 7.3g when at rest on the Earth. If this cube is now…

A: Volume of cube V=1.2 cm3 and mass of cube m=7.3 g. Now the cube is given a velocity u=0.75c say in…

Q: Particle A has half the mass and twice the speed of particle B. Is pa less than, greater than or…

A: The magnitude of the momentum(p) of a particle can be given as, p = mv, where m is the mass of the…

Q: All observers in inertial reference frames (constant relative velocities) will agree on all of the…

A: In physics, Einstein has introduced two postulated related to relativity, according to the theory of…

Q: A moving rod is observed to have a length of ℓ = 2.00 m and to be orientedat an angle of θ = 30.0°…

A: (a) The observed length of the moving rod is l = 2.00 m. The angle made by the rod with the…

Q: A supertrain of proper length 94 m travels at a speed of 0.93c as it passes through a tunnel having…

A: The Lorentz transformation is the contraction of length l of any object with respect to the moving…

Q: Earth astronomers measure that two novas (sudden brightening of a star) occur simultaneously, one in…

A: Given :-  distance of lyra and orion from earth = x2 = x1 = 2.5 x 103 cy = 2.5 E 3 cy respectively…

Q: A space traveler takes off from Earth and moves at speed 0.9900c toward the star Vega, which is…

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Q: The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a…

A: (a). the life time of moving muon is

Q: A space traveler takes off from Earth and moves at speed 0.9700c toward the star Vega, which is…

A: in this question  we use simple space motion equation  and get answer.

Q: Observers in reference frame S see an explosion located at x1= 480 m. Asecond explosion occurs 5μs…

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Q: The proper length of one spaceship is three times that of another. The two spaceships are traveling…

A: Consider The proper length of slower spaceship is "L" The proper length of faster spaceship "3L"The…

Q: ay from Earth? (b)To what frequency must Earth receivers be tuned to receive the report when the…

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Q: In the Twin Paradox, the difference in age for the twins can be accounted during which crucial…

A: Correct answer: During the period of acceleration where the traveler changes direction and returns…

Q: Starting from the Lorentz transformation, derive time dilation ?t = ? ?t0. Sketch the situation,…

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Q: An observer in reference frame S claims that two events occur simultaneously. As this observer sees…

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Q: A supertrain of proper length 100 m travels at a speed of 0.95c as it passes through a tunnel having…

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Q: The neutron has a mass of 1.67 ✕ 10−27 kg. Consider a neutron moving with a speed of 0.910c. (Enter…

A: Given:- The proton has a mass m = 1.67 ✕ 10−27 kg a proton moving with a speed of 0.910c

Q: If a m = 81.1 kg person were traveling at v = 0.980c, where c is the speed of light, what would be…

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Q: The length of a moving spaceship is 27.4 m according to an astronaut on the spaceship. If the…

A: The expression for the speed from length contraction,

Q: A cube of steel has a volume of 1.00 cm3 and mass 8.00 g when at rest on the Earth. If this cube is…

A: It is given that,

Q: The formula for length contraction gives the length of an interval on a ruler moving with velocity v…

A: Given: The formula for length contraction gives the length of an interval on a ruler moving with…

Q: a). i). What is meant by length contraction? ii). Hence, what is the length of a meterstick measured…

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Q: 1) A space traveler takes off from Earth and moves at speed 0.99c toward the star Vega, which is…

A: when an object moves with light of speed or near by difference in time frame has been noted.

Q: A spaceship of rest length 182 m races past a timing station at a speed of 0.630c. (a) What is the…

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Q: The positive muon (µ), an unstable particle, lives on average 2.20 x 10 reference) before decaying.…

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Q: Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length…

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Q: According to observer O, a blue flash occurs at ?1 = 10.4m when ?1 = 0.124µs and a red flash occurs…

A: Given : x1 = 10.4 m t1 = 0.124µs = 0.124 x 10-6 s x2 = 23.6 m t2 = 0.138µs = 0.138 x 10-6 s

Q: A rectangular painting measures 1.00 m tall and 1.50 m wide, Fig. a. It is hung on the side wall of…

A: The painting in the spaceship is at rest and hence everyone observes the painting perfectly normal.…

Q: The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6…

A: Meson Particles Meson Particles are the hadronic subatomic particles that have an equal number of…

Q: Derive the Lorentz transformation connecting a frame S (the lab frame) to a frame S′ that moves with…

A: SOlution: To derive the  Lorentz transformation connecting a frame S (the lab frame) to a frame S'.

Q: (a) A spaceship moves along the x' axis of frame S' with velocity 0.40c. Frame S' moves with…

A: Given: velocity of spaceship in frame S'  = 0.40 C velocity of frame S' with respect to S = 0.60 C

Q: Two identical particles P and Q of rest mass m,, are moving with velocities 5c 2c and 19 in…

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Q: stationary observer, jack, sees two spaceships, A and B, moving towards him from opposite directions…

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Q: According to the theory of relativity, when moving objects are measured from a stationary frame,…

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Q: If simultaneity is not an absolute concept, does that mean that we must discard the concept of…

A: Given:- If simultaneity is not an absolute concept If event A is to cause event B, A must occur…

Q: The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a…

A: a) The equation to determine the life time of the moving muon is,

Q: 1. Assuming that you are moving with a constant speed of 0.55c when you passed by a man on the…

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Q: A newly constructed spaceship has a length of 100.0 m (as measured in the rest frame). This…

A: length of spaceship = 100 m D = 50 light years v =0.9 c

Q: rocket is traveling through space and its Lorentz factor (y) is 3.9. Determine the rocket's speed…

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