frame of reference, 20 mcqs with explained answers
Here are 20 multiple-choice questions (MCQs) on Frames of Reference with explained answers for competitive exam preparation:
## Inertial Frames
1. An inertial frame of reference is one where:
- A) Newton's first law holds
- B) Objects accelerate without forces
- C) Gravity is absent
- D) Time dilation occurs
**Answer: A) Newton's first law holds**
**Explanation:** Inertial frames are those where objects at rest stay at rest and objects in motion continue in straight lines unless acted upon by forces.
2. Which frame is NOT inertial?
- A) Freely falling elevator
- B) Earth (approximately)
- C) Rotating carousel
- D) Laboratory frame
**Answer: C) Rotating carousel**
**Explanation:** Rotating frames experience fictitious centrifugal and Coriolis forces, violating Newton's first law.
3. The principle of relativity states that:
- A) All inertial frames are equivalent for mechanics
- B) Only rest frames are valid
- C) Accelerated frames are preferred
- D) Time flows differently in each frame
**Answer: A) All inertial frames are equivalent for mechanics**
**Explanation:** Galilean relativity: laws of mechanics are the same in all inertial frames.
## Non-Inertial Frames
4. In a non-inertial frame accelerating with acceleration **a**, the fictitious force on mass **m** is:
- A) **ma**
- B) -**ma**
- C) **mg**
- D) Zero
**Answer: B) -**ma****
**Explanation:** Fictitious force = -m**(frame acceleration), appearing to act opposite to frame acceleration.
5. Centrifugal force in a rotating frame is directed:
- A) Toward rotation axis
- B) Away from rotation axis
- C) Tangential to rotation
- D) Along gravity
**Answer: B) Away from rotation axis**
**Explanation:** Centrifugal force = mω²r radially outward in rotating frame.
6. Coriolis force depends on:
- A) Object's velocity in rotating frame
- B) Frame's angular velocity
- C) Both A and B
- D) Object's mass only
**Answer: C) Both A and B**
**Explanation:** Coriolis force = -2m(**ω** × **v**), depends on frame rotation ω and particle velocity **v**.
## Galilean Transformations
7. Galilean transformation for velocity between inertial frames moving at constant **V** is:
- A) **v'** = **v** + **V**
- B) **v'** = **v** - **V**
- C) **v'** = **v** × **V**
- D) **v'** = **v**/ **V**
**Answer: A) **v'** = **v** + **V****
**Explanation:** Velocities add vectorially in classical Galilean relativity.
8. Time transformation in Galilean relativity is:
- A) t' = t + Vx/c²
- B) t' = γ(t - Vx/c²)
- C) t' = t
- D) t' = t/γ
**Answer: C) t' = t**
**Explanation:** Absolute time: time intervals are same in all inertial frames (classical limit).
## Reference Frames in Mechanics
9. Foucault pendulum demonstrates:
- A) Earth's rotation (non-inertial frame)
- B) Gravitational time dilation
- C) Special relativity
- D) Quantum effects
**Answer: A) Earth's rotation (non-inertial frame)**
**Explanation:** Plane of oscillation appears to rotate due to Coriolis effect from Earth's rotation.
10. In free fall frame (elevator), effective gravity is:
- A) g upward
- B) g downward
- C) Zero
- D) 2g
**Answer: C) Zero**
**Explanation:** Equivalence principle: freely falling frame locally indistinguishable from inertial frame in absence of gravity.
## Transformations and Invariants
11. Which quantity is invariant under Galilean transformations?
- A) Velocity
- B) Time intervals
- C) Distance intervals
- D) All of these
**Answer: D) All of these**
**Explanation:** Galilean group preserves Newtonian spacetime structure (absolute time/space).
12. The most general coordinate transformation between inertial frames is:
- A) Rotation + translation + Galilean boost
- B) Only rotation
- C) Only translation
- D) Scale transformation
**Answer: A) Rotation + translation + Galilean boost**
**Explanation:** Galilean group = rotations (SO(3)) + translations + boosts.
## Applications
13. Why do we treat Earth as approximately inertial for most mechanics problems?
- A) Perfectly spherical
- B) Slow rotation (small fictitious forces)
- C) No atmosphere
- D) Uniform gravity
**Answer: B) Slow rotation (small fictitious forces)**
**Explanation:** Earth's rotation period ~24 hrs gives small ω (~7×10⁻⁵ rad/s), making fictitious forces negligible for most scales.
14. In rotating frame, equation of motion includes:
- A) Only centrifugal force
- B) Centrifugal + Coriolis
- C) Euler force (changing ω)
- D) All of these
**Answer: D) All of these**
**Explanation:** Complete non-inertial rotating frame forces: centrifugal, Coriolis, Euler.
## Advanced Concepts
15. Equivalence principle states locally:
- A) Gravity = acceleration
- B) Inertial mass = gravitational mass
- C) Both A and B
- D) Time is absolute
**Answer: C) Both A and B**
**Explanation:** Foundation of General Relativity: locally inertial frames equivalent to free fall.
16. Lorentz transformation reduces to Galilean when:
- A) v → c
- B) v << c
- C) m → 0
- D) Space is curved
**Answer: B) v << c**
**Explanation:** Low velocity limit v/c → 0 recovers classical Galilean transformations.
17. Frame dragging effect is observed in:
- A) Rotating black holes (GR)
- B) Galilean mechanics
- C) Special relativity
- D) Newtonian gravity
**Answer: A) Rotating black holes (GR)**
**Explanation:** Lense-Thirring effect: rotating mass drags spacetime, affecting inertial frames.
18. Which frame is used to define "proper time"?
- A) Laboratory frame
- B) Rest frame of clock
- C) Accelerating frame
- D) Rotating frame
**Answer: B) Rest frame of clock**
**Explanation:** Proper time is measured by clock in its instantaneous rest frame (maximal).
## Relativity of Motion
19. Newton's bucket experiment demonstrates:
- A) Absolute rotation (non-inertial effects)
- B) Time dilation
- C) Length contraction
- D) Relativity of simultaneity
**Answer: A) Absolute rotation (non-inertial effects)**
**Explanation:** Water surface curvature shows rotation relative to absolute space via centrifugal force.
20. In special relativity, inertial frames are related by:
- A) Galilean transformations
- B) Lorentz transformations
- C) Both (different limits)
- D) Conformal transformations
**Answer: B) Lorentz transformations**
**Explanation:** SR requires Lorentz invariance preserving spacetime interval ds².
