Special Relativity Practice Questions
ATAR (Australia) · ATAR Physics · 149 free MCQs with instant results and detailed explanations.
149
Total
50
Easy
78
Medium
21
Hard
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Sample Questions from Special Relativity
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Q1
Easy
What is the principle of simultaneity in special relativity?
A.
Events that are simultaneous in one frame are simultaneous in all frames.
B.
Events that are simultaneous in one frame may not be simultaneous in another frame.
C.
Simultaneity is absolute across all frames of reference.
D.
Time is experienced equally by all observers regardless of their motion.
Show Answer & Explanation
Correct Answer: B
The principle of simultaneity states that events that occur simultaneously in one inertial frame may not be simultaneous in another if the observers are in relative motion.
Q2
Easy
If a spaceship travels at 0.8c (where c is the speed of light), what is the time dilation factor experienced by passengers on the spaceship compared to observers on Earth?
A.
1.25
B.
1.67
C.
1.96
D.
0.6
Show Answer & Explanation
Correct Answer: B
The time dilation factor is given by the formula 1 / โ(1 - vยฒ/cยฒ). For v = 0.8c, the factor is 1 / โ(1 - (0.8)ยฒ) = 1 / โ(0.36) = 5/3 = 1.67.
Q3
Easy
An observer on a train moving at a constant speed sees a lightning strike at both ends of the train simultaneously. What will an observer standing on the ground conclude about the timing of the strikes?
A.
Both strikes occurred at the same time.
B.
The strike at the front of the train occurred first.
C.
The strike at the back of the train occurred first.
D.
The strikes occurred at different times but with no specific order.
Show Answer & Explanation
Correct Answer: B
Due to the motion of the train and the finite speed of light, the observer on the ground will see the lightning strike at the front of the train first, as light from the front has less distance to travel to reach them compared to the back.
Q4
Medium
A spaceship travels at 0.8c (where c is the speed of light). What is the time dilation factor experienced by astronauts on board relative to observers on Earth?
A.
1.25
B.
1.67
C.
1.33
D.
2.00
Show Answer & Explanation
Correct Answer: B
The time dilation factor is calculated using the formula ฮณ = 1 / โ(1 - vยฒ/cยฒ). Substituting v = 0.8c gives ฮณ = 1 / โ(1 - 0.64) = 1.67.
Q5
Medium
If a photon takes 2 years to travel from a distant star to Earth as observed from Earth, how much time has passed for an observer moving at 0.9c towards the star?
A.
1 year
B.
1.5 years
C.
2 years
D.
3 years
Show Answer & Explanation
Correct Answer: B
Using the relativistic Doppler effect for time, the time experienced by the moving observer is shorter due to time dilation. The relativistic factor gives 1.5 years.
Q6
Medium
Two observers are moving relative to each other at a constant velocity. If observer A measures the length of an object at rest with observer B as 10 meters, what length does observer A measure if the object is moving at 0.6c?
A.
10 meters
B.
8 meters
C.
12 meters
D.
6 meters
Show Answer & Explanation
Correct Answer: B
In the case of length contraction, the length measured by the observer moving relative to the object is shorter. The formula is L = L0โ(1 - vยฒ/cยฒ). Here, L0 = 10 m, v = 0.6c, so L = 10โ(1 - 0.36) = 10โ0.64 = 10 ร 0.8 = 8 meters.
Q7
Medium
A spaceship travels at 0.8c (where c is the speed of light). What is the time dilation factor experienced by the astronauts on board compared to observers on Earth?
A.
1.25
B.
1.67
C.
2.5
D.
3.0
Show Answer & Explanation
Correct Answer: B
The time dilation factor can be calculated using the formula ฮณ = 1 / โ(1 - vยฒ/cยฒ). For v = 0.8c, ฮณ = 1 / โ(1 - (0.8)ยฒ) = 1.67, meaning time passes slower for the astronauts compared to observers on Earth.
Q8
Hard
A particle is moving at a speed of 0.9c. If the particle emits a photon in the forward direction, what will be the speed of the photon as observed from a stationary frame?
A.
0.9c
B.
c
C.
1.8c
D.
0.1c
Show Answer & Explanation
Correct Answer: B
According to the principles of special relativity, the speed of light is always constant in a vacuum and is measured as 'c' in all inertial frames. Therefore, regardless of the speed of the particle, the speed of the emitted photon remains c.
Q9
Hard
A particle moving at 0.9c emits two photons in opposite directions. How does the energy measured by a stationary observer compare to the energy measured by the particle's frame?
A.
The energy measured by the stationary observer is less than that in the particle's frame.
B.
The energy measured by the stationary observer is equal to that in the particle's frame.
C.
The energy measured by the stationary observer is greater than that in the particle's frame.
D.
The energy cannot be determined without knowing the frequency of the photons.
Show Answer & Explanation
Correct Answer: C
Due to the relativistic Doppler effect, the stationary observer perceives the photons emitted in the direction of motion to have higher energy, while the ones emitted in the opposite direction will have lower energy. Overall, this results in a total energy greater than in the particle's frame.
Q10
Hard
A spaceship travels at a speed of 0.8c (where c is the speed of light). If the proper length of the spaceship is 100 meters, what is the observed length of the spaceship from a stationary observer's perspective according to the Lorentz contraction formula?
A.
60 meters
B.
80 meters
C.
100 meters
D.
125 meters
Show Answer & Explanation
Correct Answer: A
According to the Lorentz contraction formula, L = L0 * sqrt(1 - v^2/c^2). Here, L0 = 100 meters, v = 0.8c. Thus, L = 100 * sqrt(1 - (0.8)^2) = 100 * sqrt(1 - 0.64) = 100 * sqrt(0.36) = 100 * 0.6 = 60 meters.
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Special Relativity โ ATAR (Australia) ATAR Physics Practice Questions Online
This page contains 149 practice MCQs for the chapter Special Relativity in ATAR (Australia) ATAR Physics. The questions are organized by difficulty โ 50 easy, 78 medium, 21 hard โ so you can choose the right level for your preparation.
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