Q1. According to Galilean relativity, the laws of mechanics are the same in:

All accelerating frames
All inertial frames
Only a frame at absolute rest
Only rotating frames

Q2. An inertial frame of reference is one in which:

Every object is at rest
Gravity is absent
Newton's first law is valid
Time does not pass

Q3. Suppose frame \(S'\) moves with constant velocity \(v\) along the positive \(x\)-direction relative to \(S\). The Galilean transformation for position is:

\(x'=x+vt\)
\(x'=x-vt\)
\(x'=vt-x^2\)
\(x'=x/vt\)

Q4. According to the Galilean transformation:

\(t'=t-vx/c^2\)
\(t'=\gamma t\)
\(t'=t\)
\(t'=t/\gamma\)

Q5. Under Galilean velocity transformation, if \(u_x\) is the velocity in \(S\), then the velocity measured in \(S'\) is:

\(u'_x=u_x+v\)
\(u'_x=u_x-v\)
\(u'_x=u_xv\)
\(u'_x=u_x/v\)

Q6. A train moves at \(20\,\text{m/s}\). A person inside the train throws a ball forward at \(5\,\text{m/s}\) relative to the train. According to Galilean relativity, the ball's speed relative to the ground is:

\(5\,\text{m/s}\)
\(15\,\text{m/s}\)
\(25\,\text{m/s}\)
\(100\,\text{m/s}\)

Q7. A major difficulty in applying Galilean transformations to electromagnetism is that:

Newton's laws become invalid at low speeds
Maxwell's equations are not invariant under Galilean transformations
Electric charges disappear
Magnetic fields cannot exist

Q8. Maxwell's theory predicts that electromagnetic waves in vacuum travel with speed:

Depending on the speed of the source
Depending on the observer's speed
\(c=1/\sqrt{\mu_0\epsilon_0}\)
Zero in vacuum

Q9. The Michelson-Morley experiment was designed to detect:

Gravitational waves
Electrons
The motion of Earth through the hypothetical luminiferous ether
Nuclear radiation

Q10. The Michelson-Morley experiment used a device known as:

Spectrometer
Cyclotron
Interferometer
Calorimeter

Q11. The main result of the Michelson-Morley experiment was:

A large ether wind was detected
No expected ether-wind effect was detected
The speed of light was found to be zero
Newton's law of gravitation was disproved

Q12. Einstein's first postulate of special relativity states that:

There exists an absolute frame of rest
The laws of physics have the same form in all inertial frames
Only the laws of mechanics are invariant
Time is absolute

Q13. Einstein's second postulate states that the speed of light in vacuum:

Depends on the speed of the source
Depends on the observer
Has the same value \(c\) for all inertial observers
Is infinite

Q14. The Lorentz factor is defined as:

\(\gamma=\sqrt{1-v^2/c^2}\)
\(\displaystyle \gamma=\frac{1}{\sqrt{1-v^2/c^2}}\)
\(\gamma=1-v/c\)
\(\gamma=c/v\)

Q15. The Lorentz transformation for \(x\), when \(S'\) moves with speed \(v\) along the \(x\)-axis, is:

\(x'=x-vt\)
\(x'=\gamma(x-vt)\)
\(x'=\gamma(x+vt)\)
\(x'=x/\gamma\)

Q16. The Lorentz transformation of time is:

\(t'=t\)
\(t'=\gamma(t-vx)\)
\(\displaystyle t'=\gamma\left(t-\frac{vx}{c^2}\right)\)
\(t'=t-v/c\)

Q17. When \(v\ll c\), the Lorentz transformation approximately reduces to:

Newton's law of gravitation
Galilean transformation
Maxwell's equations
Kepler's transformation

Q18. The relativistic velocity transformation for motion along the \(x\)-direction is:

\(u'_x=u_x-v\)
\(\displaystyle u'_x=\frac{u_x-v}{1-u_xv/c^2}\)
\(u'_x=u_x+v\)
\(u'_x=u_xv/c\)

Q19. A spaceship moves at \(0.6c\) relative to Earth and emits light forward. The speed of this light measured on Earth is:

\(0.4c\)
\(0.6c\)
\(c\)
\(1.6c\)

Q20. Two spaceships approach each other. One moves at \(0.6c\) and the other at \(0.6c\) relative to Earth in opposite directions. The speed of one measured from the other is:

\(1.2c\)
\(0.6c\)
\(\displaystyle \frac{1.2c}{1+0.36}\approx0.882c\)
\(0.36c\)

Q21. The proper length of an object is its length measured:

When the object moves at speed \(c\)
In the frame in which the object is at rest
Only from Earth
By an accelerating observer

Q22. The formula for relativistic length contraction is:

\(L=\gamma L_0\)
\(\displaystyle L=\frac{L_0}{\gamma}=L_0\sqrt{1-v^2/c^2}\)
\(L=L_0(1+v/c)\)
\(L=L_0\)

Q23. A spaceship has a proper length of \(100\,\text{m}\). If it moves with \(\gamma=2\), its length measured from Earth is:

\(200\,\text{m}\)
\(50\,\text{m}\)
\(100\,\text{m}\)
\(25\,\text{m}\)

Q24. Length contraction occurs:

In all directions equally
Only along the direction of relative motion
Only perpendicular to motion
Only for light

Q25. The proper time between two events is measured by a clock:

Moving at speed \(c\)
For which the two events occur at the same spatial position
At an arbitrary distance from both events
Only on Earth

Q26. The time-dilation relation is:

\(\Delta t=\Delta\tau/\gamma\)
\(\Delta t=\gamma\Delta\tau\)
\(\Delta t=\Delta\tau\sqrt{1-v/c}\)
\(\Delta t=\Delta\tau\)

Q27. A moving clock is observed from an inertial frame in which it is moving. Compared with clocks at rest in that frame, the moving clock appears to:

Run faster
Run slower
Stop completely at every speed
Run at twice the rate

Q28. If the proper time interval is \(5\,\mu s\) and \(\gamma=2\), the time interval measured in a frame where the clock is moving is:

\(2.5\,\mu s\)
\(5\,\mu s\)
\(10\,\mu s\)
\(20\,\mu s\)

Q29. In special relativity, two events that are simultaneous in one inertial frame:

Must be simultaneous in every inertial frame
Need not be simultaneous in another inertial frame
Must occur at the same position
Cannot be observed

Q30. Relativity of simultaneity follows directly from the Lorentz transformation of:

Mass only
Energy only
Time
Electric charge

Q31. The modern relativistic expression for the momentum of a particle of invariant mass \(m\) is:

\(p=mv\)
\(p=\gamma mv\)
\(p=mc^2\)
\(p=m/v\)

Q32. The rest energy of a particle of invariant mass \(m\) is:

\(E_0=mc\)
\(E_0=mc^2\)
\(E_0=mv^2\)
\(E_0=m/c^2\)

Q33. The total relativistic energy of a particle is:

\(E=mv^2\)
\(E=mc^2\)
\(E=\gamma mc^2\)
\(E=\gamma mv\)

Q34. The relativistic kinetic energy of a particle is:

\(K=\gamma mc^2\)
\(K=(\gamma-1)mc^2\)
\(K=mc^2/\gamma\)
\(K=(1-\gamma)mc^2\)

Q35. The relativistic energy-momentum relation is:

\(E=pc\)
\(E^2=p^2c^2+m^2c^4\)
\(E^2=p^2+m^2\)
\(E=p^2/2m\)

Q36. If a particle has zero invariant mass, the energy-momentum relation becomes:

\(E=mc^2\)
\(E=pc\)
\(E=p/c\)
\(E=0\)

Q37. Nuclear binding energy is related to the mass defect \(\Delta m\) by:

\(B=\Delta m/c^2\)
\(B=\Delta mc\)
\(B=\Delta mc^2\)
\(B=\Delta mv\)

Q38. If a nuclear reaction has a mass defect of \(1\,u\), the corresponding energy is approximately:

\(9.31\,\text{MeV}\)
\(93.1\,\text{MeV}\)
\(931.5\,\text{MeV}\)
\(9315\,\text{MeV}\)

Q39. Nuclear fission is the process in which:

Two light nuclei combine
A heavy nucleus splits into lighter nuclei
An electron combines with a positron only
A photon loses all its energy without interaction

Q40. Nuclear fusion is the process in which:

A heavy nucleus splits into smaller nuclei
Light nuclei combine to form a heavier nucleus
Matter is completely destroyed
An electron becomes a photon

Q41. The primary source of the Sun's energy is:

Nuclear fission
Nuclear fusion
Chemical combustion
Gravitational repulsion

Q42. Pair production can produce an electron and a positron from:

A low-energy sound wave
A sufficiently energetic photon in the presence of a nucleus or other body that can take recoil
A stationary electron alone
A magnetic field with no energy input

Q43. Since the rest energy of an electron is approximately \(0.511\,\text{MeV}\), the threshold photon energy for electron-positron pair production near a heavy nucleus is approximately:

\(0.511\,\text{MeV}\)
\(1.022\,\text{MeV}\)
\(2.044\,\text{MeV}\)
\(0.255\,\text{MeV}\)

Q44. The principle of equivalence states, locally, that the effects of a uniform gravitational field are indistinguishable from those of:

Uniform velocity
Appropriate uniform acceleration
Circular motion only
Zero mass

Q45. A person inside a closed elevator in free fall would locally experience:

Twice the normal weight
Apparent weightlessness
Infinite weight
No inertia

Q46. According to general relativity, a light ray passing near a massive body:

Must continue along an exactly straight Euclidean line
Is deflected by the gravitational field
Comes to rest
Becomes a massive particle

Q47. The bending of starlight near the Sun was famously tested during:

A lunar eclipse
A total solar eclipse
A meteor shower
A planetary transit only

Q48. The approximate deflection angle predicted by general relativity for light grazing the surface of the Sun is:

\(0.175''\)
\(0.875''\)
\(1.75''\)
\(17.5''\)

Q49. The general relativistic deflection angle for light passing a spherical mass \(M\) with impact parameter \(b\) in the weak-field limit is:

\(\displaystyle \frac{GM}{bc^2}\)
\(\displaystyle \frac{2GM}{bc^2}\)
\(\displaystyle \frac{4GM}{bc^2}\)
\(\displaystyle \frac{GMb}{c^2}\)

Q50. Which statement correctly describes the progression from Galilean relativity to special and general relativity?

Special relativity applies only to gravity
General relativity restores absolute space and absolute time
Galilean relativity is the low-speed approximation, special relativity describes inertial frames consistently with invariant \(c\), and general relativity extends relativity to gravitation
The three theories make identical predictions at all speeds and gravitational fields