Q: A spaceship travels at $$0.8c$$ relative to Earth. If its proper length is $$L_0 = 100$ m, what length does an observer on Earth measure?

$$L = L_0$ \sqrt{1 - \frac{v^2$}{c^2$}} = 100 \times \sqrt{1 - \frac{0.8^2$}{1^2$}} = 60 m$$

Question 1

Which experiment disproved the existence of the 'ether' as a medium for light propagation and confirmed that the speed of light is independent of the observer's motion?

Accepted Answer

The Michelson-Morley interference experiment

Question 2

According to the first postulate of special relativity, what is true about the laws of physics?

Accepted Answer

They are the same in all inertial frames of reference

Question 3

A spaceship travels at $$0.8c$$ relative to Earth. If its proper length is $$L_0 = 100$ m, what length does an observer on Earth measure?

Accepted Answer

$$L = L_0$ \sqrt{1 - \frac{v^2$}{c^2$}} = 100 	imes \sqrt{1 - \frac{0.8^2$}{1^2$}} = 60 m$$

Question 4

If an astronaut travels away from Earth at a speed close to $$c$$, how would an observer on Earth measure the astronaut’s pulse rate?

Accepted Answer

It would be slower

Question 5

What is the formula for time dilation in special relativity?

Accepted Answer

$$T = \frac{T_0$}{\sqrt{1 - \frac{v^2$}{c^2$}}}$$

Question 6

A pendulum in a spaceship has a period of 2 seconds when parked on Earth. What is its period for an observer on Earth when the spaceship moves at $$0.6c$$?

Accepted Answer

More than 2 seconds

Question 7

Which equation expresses the relativistic addition of velocities for two objects moving in the same direction?

Accepted Answer

$$u' = \frac{u + v}{1 + \frac{uv}{c^2$}}$$

Question 8

A spear is thrown at a speed such that its measured length is half its proper length. What is its relativistic mass compared to its rest mass?

Accepted Answer

Twice its rest mass

Question 9

Which of the following is a prediction of general relativity?

Accepted Answer

Gravitational lensing

Question 10

What is the formula for the total energy of an object in special relativity?

Accepted Answer

$$E = mc^2$

Question 11

A train moves at $$0.9c$$ and fires a laser forward. What is the speed of the laser beam relative to the ground?

Accepted Answer

$$c$$

Question 12

Which concept explains why GPS satellites must account for relativistic effects?

Accepted Answer

Time dilation due to their high speed and gravitational field differences

Question 13

What happens to the length of a spaceship as its speed approaches the speed of light, as observed from Earth?

Accepted Answer

It becomes shorter and shorter

Question 14

Which equation describes the relativistic momentum of an object?

Accepted Answer

$$p = \gamma m_0$ v$$

Question 15

In the context of general relativity, what does the principle of equivalence state?

Accepted Answer

All physical experiments in a uniform gravitational field and in an accelerated frame give identical results

Question 16

If two spaceships approach each other, each at $$0.75c$$ relative to the ground, what is their relative speed according to special relativity?

Accepted Answer

$$v_{rel} = \frac{0.75c + 0.75c}{1 + \frac{(0.75c)(0.75c)}{c^2$}} \approx 0.96c$$

Question 17

Which of the following is NOT affected by length contraction?

Accepted Answer

Distances perpendicular to the direction of motion

Question 18

What is the rest energy of an object with rest mass $$m_0$$?

Accepted Answer

$$E_0$$ = $$m_0$$ $$c^2$$

Question 19

Which real-world phenomenon is explained by the curvature of space-time around massive objects?

Accepted Answer

Gravitational lensing

Question 20

If a conductor moves through a magnetic field, what is observed in the reference frame of the conductor according to classical mechanics?

Accepted Answer

No magnetic force acts on the charges and no electric field is generated

Chapter 29: Relativity – Study Notes for General Physics II

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