Special Theory Of Relativity MCQ Level – 1 - IIT JAM MCQ

On solving

The correct answer is: 0.85 c

Length contraction: L = L₀/γ
with γ = 1/(1 − ^v2/_c²)^½ 

Given for the car, L₀ = 5 m and L = 3 m

γ = L₀/L = 5/3 = 1/(1 − ^v2/_c²)^½ 
γ² = 25/9 = 1/(1 − ^v2/_c²)
1 − v²/c² = 9/25
v²/c² = 1 − 9/25 = 16/25
v = ⁴/₅ c = 0.8c

∆t = t / √(1-v²/c²)

∆t = 2*10^-8/√(1-(0.8)²)

∆t = 2*10^-8 / 0.6

∆t = 3.3*10^-8 s

dS²  = dr² + (cdt)²  =  dx² + dy² + dz² − (cdt)² 
dS² = dS'² 

dx² = (5 − 3)² = 4
dy² = (3 − 3)² = 0
dz² = (1 − 3)² = 4
dt²  = (5 − 3)² = 4
c = 1

dS'² = 4 + 0 + 4 − 4 = 4
dS' = 2

Since the light received has a higher wavelength than the incident wavelength, one concludes that this is a red shift, that the object is moving away from the Earth.

where λ₀ is the wavelength of the source.
The doppler effect equation gives 

Solving this one gets β = 35/37

v = 2.8 × 10⁸ m/s
away from the Earth.

The correct answer is: 2.8 × 10⁸ m/s away from Earth

Total energy = 10 GeV
p = 8 GeV

In units in which c = 1 option (d)

The correct answer is: 6 GeV/c²

The form of the matrix show that the rotation is about the z-axis

since 

since the z component does not change
∴  rotation about the z axis

Now, the standard from of the rotation matrix about z axis is

The correct answer is: 60° counter clockwise about the z axis

Correct Answer :- d

Explanation : The order of the door opening depends on which reference frame one is in

So, the car fits in the garage’s frame (the car is 3m  and the garage is 4m). But in its own frame, the car is much longer to fit in the garage (car is 5m  and the garage is only 2.4m)

Both the frames give different answers.

There is no unique answer, as the order of door openings and closings depends on the reference frame.

The mass of the rod is 3/2 times its rest mass, that is

The length of meter stick moving parallel to its length, according to length contraction formula.

L₀ = 1m
L = 1 × 0.667 = 0.67m
The correct answer is: 0.67 m

1000 x 3600 x v / √ 1- v²/ c² = 1.08 x 10¹² x 1000

= 105 x 36 x v / √ 1- v²/ c² = 1080 x 10¹²

= v / √ 1- v²/ c² = c

v = c / √2