Question 1

The Michelson-Morley experiment, as depicted in the first image, was designed to detect differences in the speed of light due to Earth's motion through space. What was the outcome and its significance for the development of special relativity?

Accepted Answer

It detected no difference, supporting the idea that the speed of light is constant in all frames of reference.

Question 2

According to Einstein's first postulate of special relativity, which of the following statements is true?

Accepted Answer

The laws of nature are the same in all uniformly moving frames of reference.

Question 3

A spaceship moves at a speed $$v = 0.8c$$ relative to Earth. According to the length contraction formula $$L = L_0$ \sqrt{1 - \frac{v^2$}{c^2$}}$$, what happens to the length of the spaceship as measured by an observer on Earth?

Accepted Answer

It appears shorter than its rest length.

Question 4

Which equation correctly describes the relativistic addition of velocities?

Accepted Answer

$$V = \frac{v_1$ + v_2$}{1 + \frac{v_1$ v_2$}{c^2$}}$$

Question 5

If two events are simultaneous in one frame of reference, what can be said about their simultaneity in another frame moving relative to the first?

Accepted Answer

They may not be simultaneous in the moving frame.

Question 6

A light clock is moving at speed $$v$$ relative to an observer. According to the observer, the time between ticks is given by $$t = \frac{t_0$}{\sqrt{1 - \frac{v^2$}{c^2$}}}. $$What does this imply about the passage of time on the moving clock?

Accepted Answer

Time passes more slowly on the moving clock.

Question 7

In the famous 'twin paradox,' one twin travels at high speed in space and returns younger than the twin who stayed on Earth. What is the main reason for this age difference?

Accepted Answer

The traveling twin's clock ran slower due to time dilation.

Question 8

Which of the following best describes the correspondence principle as it applies to special relativity?

Accepted Answer

Special relativity agrees with classical mechanics at low speeds.

Question 9

A particle moves at $$0.9c$$ and has a rest mass $$m. $$What is its relativistic momentum?

Accepted Answer

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

Question 10

A nuclear power plant converts $$1$$ gram of mass into energy. Using $$E = mc^2$, how much energy is released? (c = 3$$ 	imes $$10^8 m/s)$$

Accepted Answer

$$9 	imes 10$$^{13}$$ J

Question 11

If an astronaut travels at $$0.99c$$ for what appears to be 10 years on Earth, how much time passes for the astronaut? Use $$t = \frac{t_0$}{\sqrt{1 - \frac{v^2$}{c^2$}}}.$$

Accepted Answer

Much less than 10 years

Question 12

Which of the following is a direct consequence of the invariance of the speed of light for all observers?

Accepted Answer

Time and space measurements depend on the observer's frame of reference.

Question 13

A spaceship passes Earth at $$0.6c. $$According to an observer on Earth, a clock on the spaceship ticks once every 10 seconds. What is the proper time interval between ticks on the spaceship?

Accepted Answer

8 seconds

Question 14

Which of the following statements about length contraction is correct?

Accepted Answer

Length contraction occurs only in the direction of motion.

Question 15

If a spaceship emits flashes every 6 minutes while approaching Earth at constant speed, how will these flashes be spaced when received on Earth?

Accepted Answer

They will be equally spaced less than 6 minutes apart.

Question 16

Why can't we say that the spaceship is at rest and the Earth moves, so the Earth twin ages less in the twin paradox?

Accepted Answer

Because the traveling twin experiences acceleration and changes frames.

Question 17

Which of the following best describes the relationship between mass and energy according to special relativity?

Accepted Answer

Energy and mass are equivalent and related by $$E = mc^2$.

Question 18

A subatomic particle is accelerated to near the speed of light. Compared to its Newtonian momentum, its relativistic momentum is:

Accepted Answer

Greater than the Newtonian value.

Question 19

Which of the following is NOT a postulate of special relativity?

Accepted Answer

The speed of light depends on the motion of the source.

Special Theory of Relativity: Structured Study Notes

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