Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Physics : Special Relativity

Study concepts, example questions & explanations for GRE Subject Test: Physics

Create An Account

All GRE Subject Test: Physics Resources

33 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Special Relativity

The difference in age for the twins in the Twin Paradox occurs during which key moment in the trip?

Possible Answers:

During the beginning of the journey traveling fast.

During the period of great acceleration during the changing of directions and return to Earth.

While approaching a black hole in space during the trip.

During the time returning to Earth traveling fast.

None of these

Correct answer:

During the period of great acceleration during the changing of directions and return to Earth.

Explanation:

While moving clocks do in fact record time moving at different rates, the time dilation works both ways. This means that a stationary person will view a moving clock ticking slower, but at the same time, a person moving alongside the moving clock will see the stationary clock ticking slower. However, clocks experiencing great accelerations will be permanently changed, "losing" time relative to a clock not being accelerated. Thus, the age difference occurs during the portion of the journey when the traveler accelerates at a great rate in order to return to Earth.

Report an Error

Example Question #1 : Special Relativity

A black hole is an object whose gravitational field is so strong that even light cannot escape. Assuming no change in radius, approximately how much mass would our Sun have to have in order to become a black hole?

Sun's radius: $R=6.963\times10^{8}\,\textup{m}$

Possible Answers:

$1.5\times10^{27}\,\textup{kg}$

$1\times10^{35}\,\textup{kg}$

$2\times10^{30}\,\textup{kg}$

$5\times10^{35}\,\textup{kg}$

$3\times10^{40}\,\textup{kg}$

Correct answer:

$5\times10^{35}\,\textup{kg}$

Explanation:

To derive the Schwarzschild radius of a black hole, set gravitational potential energy equal to kinetic energy at escape velocity:

$\frac{GMm}{r}=\frac{1}{2}mc^2$

Solving for mass of the black hole:

$M=\frac{rc^2}{2G}=\frac{(6.963\times 10^8 \textup{m})(2.998\times 10^8 \textup{m\,s}^{-1})^2}{2(6.674 \times 10^{-11}\textup{m}^3\,\textup{kg}^{-1}\textup{s}^{-2})} =5\times10^{35}\,\textup{kg}$

Report an Error

Example Question #3 : Special Relativity

At one point in time, two twins are 30 years old. At this time, one of them gets on a rocket and travels at 0.8 c, for what he experiences to be 12 years. How old is the twin that remained on Earth when the traveling twin returns home?

Possible Answers:

37 years old

50 years old

42 years old

70 years old

Correct answer:

50 years old

Explanation:

The equation for time dilation is given by:

$T'=\frac{T}{\sqrt{1-\frac{v^2}{c^2}}}$

In this problem v=0.8c T=12. Using this equation, we get:

$T'=\frac{12}{\sqrt{1-(\frac{4}{5})^2}}=\frac{12}{\sqrt{1-\frac{16}{25}}}=\frac{12}{\sqrt{\frac{9}{25}}} =\frac{12}{\frac{3}{5}}=(12)(\frac{5}{3})=20$

Adding 20 years to the age initial age of 30:

30+20=50

The Earth-twin is now 50.

Report an Error

Example Question #1 : Special Relativity

A meter stick, at an angle of 30 degrees with the x-axis, is traveling at 0.6c in the direction of the positive y-axis. To a stationary observer, how long does the meter stick appear to be?

Possible Answers:

$\frac{1}{5}\sqrt{\frac{29}{2}}\textup{m}$

$\frac{\sqrt{91}}{10}\textup{m}$

$1\textup{m}$

$\sqrt{\frac{31}{42}}\textup{m}$

$\frac{4}{5}\textup{m}$

Correct answer:

$\frac{\sqrt{91}}{10}\textup{m}$

Explanation:

Length contraction only occurs in the direction of motion. This means that the x component of the length, which is cos(30), does not change; length contraction only occurs the the y component, which is sin(30).

First, we find the Lorentz factor:

$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{1}{\sqrt{1-\frac{9}{25}}}=\frac{1}{\sqrt{\frac{16}{25}}}=\frac{5}{4}$

Next, we apply the time dilation equation to the length in the y direction:

$L'_y=L_{y}/ \gamma=\frac{4}{5}\sin(30)=\frac{2}{5}$

Finally, we find the total length by combining the length-contracted y component and the unchanged x component:

$L=\sqrt{L_x^2+L'_y^2}=$ $\sqrt{\frac{3}{4}+\frac{4}{25}}=\frac{\sqrt{91}}{10}$

Report an Error

Example Question #4 : Special Relativity

A rocket of length 5 meters passes an observer on earth. The observer measures the passing rocket to be 3 meters long. What is the velocity of the rocket in the reference frame of the Earth-based observer?

Possible Answers:

0.75c

0.4c

0.8 c

0.6c

1.25c

Correct answer:

0.8 c

Explanation:

Length contraction is given by

$L_{rest}=\gamma L_{move}$

Where in this case,

$L_{rest}=5\textup{m}, \,\,\,L_{move}=3\textup{m}$

The Lorentz factor is given by:

$\gamma=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

Combining these two equations, we get:

$L_{rest}=\frac{L_{move}}{\sqrt{1-\frac{v^2}{c^2}}}$

Solving for v:

$v=c\sqrt{1-\left ( \frac{L_{move}}{L_{rest}}\right )^2}= c\sqrt{1-\left ( \frac{3}{5}\right )^2}= c\sqrt{1-\left ( \frac{9}{25}\right )}$

$= c\sqrt{\left( \frac{16}{25}\right )}=\frac{4}{5}c=0.8c$

Report an Error

Example Question #1 : Special Relativity

A relativistic particle of mass m has a total energy 37 times its rest energy. What is the momentum of the particle, in units of mc?

Possible Answers:

144

Correct answer:

Explanation:

The total energy E of a relativistic particle is related to its rest mass energy E_o by:

$E=\gamma E_{o}$

Where gamma is related to the momentum by:

$p=\gamma mc$

Combining the equations and solving for p, we get:

$p=\frac{E}{E_{o}}mc=37 mc$

Which, in the units specified, is 37.

Report an Error

Example Question #2 : Special Relativity

A particle of mass m traveling at a relativistic speed has a momentum of 50 mc. What is the total energy E of the particle, expressed in units of the rest mass energy E_o?

Possible Answers:

50 E_o

75 E_o

5 E_o

$5\sqrt{2}E_o$

2500 E_o

Correct answer:

50 E_o

Explanation:

For a relativistic particle, momentum is given by:

$p=\gamma mc$

from which we can solve for gamma:

$\gamma=\frac{p}{mc}=\frac{50 mc}{mc}=50$

Total energy of a relativistic particle is given by:

$E=\gamma E_{o}=50E_{0}$

Report an Error

Example Question #1 : Energy And Momentum

The rest mass energy E_o of a particle with mass is one quarter of its total energy . What is the of the particle's momentum, in units of ?

Possible Answers:

$\sqrt{3}$

$\sqrt{15}$

Correct answer:

$\sqrt{15}$

Explanation:

The question tells us:

$E=4E_{o}$

Where the rest mass energy of a particle is:

$E_{o}=mc^{2}$

Using the equation for the total energy of a particle, we can substitute:

$E=\sqrt{p^{2}c^{2}+m^{2}c^{4}}$

$4mc^2=\sqrt{p^2c^2+m^2c^4}$

Solving this for , we find:

$p=\sqrt{15m^2c^2}=\sqrt{15}\,\,mc$

Which, in units of mc, gives us the correct answer.

Report an Error

Example Question #3 : Special Relativity

The relativistic momentum of a particle with mass is 3mc . What is the total energy of the particle, given in units of the rest mass energy E_o ?

Possible Answers:

$4E_{o}$

$\sqrt{10}E_{o}$

$10E_{o}$

$2E_{o}$

$\sqrt{2}E_{o}$

Correct answer:

$\sqrt{10}E_{o}$

Explanation:

The total energy of a relativistic particle is given by:

$E=\sqrt{p^2c^2+m^2c^4}$

Substituting the momentum, we get:

$E=\sqrt{9m^2c^4+m^2c^4}=\sqrt{10}mc^2$

Because the rest mass energy of a particle is given by:

$E_{o}=mc^2$

The total energy is:

$E=\sqrt{10}E_{o}$

Report an Error

Example Question #6 : Special Relativity

A scientist measures the spectrum of relativistic jet emitted from a black hole. He finds that the a particular spectral line, which has a stationary wavelength of 212.5 nm, has a Doppler shifted wavelength of 643.7 nm. What is the radial velocity of the relativistic jet?

Possible Answers:

$2.4*10^8 \frac{m}{s} \textup{ towards the Earth}$

$3.2*10^8 \frac{m}{s} \textup{ towards the Earth}$

$2.2*10^8 \frac{m}{s}\textup{ away from the Earth}$

$2.2*10^8 \frac{m}{s}\textup{ towards the Earth}$

$2.4*10^8 \frac{m}{s} \textup{ away from the Earth}$

Correct answer:

$2.4*10^8 \frac{m}{s} \textup{ away from the Earth}$

Explanation:

The relativistic Doppler shift equation is given by:

$\lambda_{moving}=\frac{\sqrt{1+\beta}}{\sqrt{1-\beta}}\lambda_{stationary}$

Where $\beta$ is defined as:

$\beta=\frac{v_{source}}{c}$

Because the stationary wavelength is shorter than the moving wavelength, the object must be receding from the Earth, eliminating two answers.

The speed of light is approximately $3*10^8 \frac{m}{s}$ , so $3.2*10^8 \frac{m}{s}$ is not a possible answer.

Making the approximation that

$\frac{\lambda_{m}}{\lambda_{s}}=\frac{643.7}{212.5}\approx3$

Combining this with the first equation:

$\frac{\lambda_m}{\lambda_s}=\frac{\sqrt{1+\beta}}{\sqrt{1-\beta}}=3$

$3\sqrt{1-\beta}=\sqrt{1+\beta}$

$9(1-\beta)=1+\beta$

$9-9\beta=1+\beta$

$10\beta=8,\,\,\,\beta=0.8$

From beta, we can find the velocity:

$\beta=\frac{v_{source}}{c}\rightarrow v_{source}=\beta c=(0.8)(3\times10^8 \frac{m}{s})=2.4\times10^8 \frac{m}{s}$

Report an Error

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Nafis
Certified Tutor

University of Leipzig, Germany., Bachelor of Science, Physics. University of Pittsburgh-Pittsburgh Campus, Doctor of Philosop...

All GRE Subject Test: Physics Resources

33 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Philadelphia, Math Tutors in Dallas Fort Worth, SAT Tutors in Dallas Fort Worth, Calculus Tutors in Boston, LSAT Tutors in Denver, French Tutors in Dallas Fort Worth, Reading Tutors in Houston, Physics Tutors in Denver, Reading Tutors in Philadelphia, SSAT Tutors in Boston

Popular Courses & Classes

Spanish Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Chicago, LSAT Courses & Classes in Boston, ISEE Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Los Angeles, MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in New York City

Popular Test Prep

ISEE Test Prep in San Diego, GMAT Test Prep in Washington DC, SSAT Test Prep in Denver, ACT Test Prep in New York City, MCAT Test Prep in Houston, SSAT Test Prep in Washington DC, SAT Test Prep in Chicago, MCAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Miami, SAT Test Prep in Houston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

GRE Subject Test: Physics : Special Relativity

Study concepts, example questions & explanations for GRE Subject Test: Physics

All GRE Subject Test: Physics Resources

Example Questions

Example Question #1 : Special Relativity

Example Question #1 : Special Relativity

Example Question #3 : Special Relativity

Example Question #1 : Special Relativity

Example Question #4 : Special Relativity

Example Question #1 : Special Relativity

Example Question #2 : Special Relativity

Example Question #1 : Energy And Momentum

Example Question #3 : Special Relativity

Example Question #6 : Special Relativity

All GRE Subject Test: Physics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: