Here are 20 multiple-choice questions (MCQs) on central and non-central forces with explained answers:
1. A central force depends on:
- A) Position vector only
- B) Velocity only
- C) Both position and velocity
- D) Time only
Answer: A. Central forces depend only on distance from center and act along line joining particles [1].
2. Which force is central?
- A) Frictional force
- B) Gravitational force
- C) Magnetic force on moving charge
- D) Tension in string (directional)
Answer: B. Gravity acts along line joining masses, magnitude depends on distance [1].
3. Central forces conserve:
- A) Linear momentum
- B) Angular momentum
- C) Energy only
- D) None
Answer: B. Torque is zero (r × F = 0) so angular momentum is conserved [2].
4. Non-central forces produce:
- A) Circular orbits only
- B) Torque about center
- C) Conserved angular momentum
- D) Radial motion only
Answer: B. Non-central forces have component perpendicular to radius vector, producing torque [3].
5. Which is NOT a central force?
- A) Electrostatic force
- B) Nuclear force
- C) Coriolis force
- D) Gravitational force
Answer: C. Coriolis force is velocity-dependent and perpendicular to velocity [4].
6. For central force, motion lies in:
- A) 3D plane
- B) Fixed plane
- C) Random plane
- D) Spherical surface
Answer: B. Angular momentum conservation keeps motion in single plane [1].
7. Mathematical form of central force:
- A) F = f(r) (radial)
- B) F = f(r, θ, φ)
- C) F has tangential component
- D) F ∝ velocity
Answer: A. Central force F = f(r) \hat{r}, purely radial [2].
8. Which conserves angular momentum?
- A) All forces
- B) Central forces only
- C) Non-central forces only
- D) Contact forces
Answer: B. Only central forces produce zero torque [1].
9. Example of non-central force:
- A) Coulomb force
- B) Force on charge in magnetic field
- C) Spring force
- D) Universal gravitation
Answer: B. Magnetic force F = q(v × B) is perpendicular to both v and B [4].
10. Orbital motion is possible with:
- A) Non-central forces only
- B) Central forces only
- C) Both types
- D) Neither
Answer: B. Stable closed orbits require central forces [2].
11. If F is central, then dL/dt equals:
- A) F × r
- B) r × F
- C) Zero
- D) mv
Answer: C. Torque τ = r × F = 0 for central forces, so dL/dt = 0 [1].
12. Which force pair are both central?
- A) Gravity and friction
- B) Electrostatic and gravitational
- C) Magnetic and tension
- D) Drag and spring
Answer: B. Both electrostatic and gravitational are inverse square central forces [3].
13. Non-central forces cause:
- A) Precession of orbits
- B) Circular motion
- C) Stable elliptical orbits
- D) Conservation of L
Answer: A. Non-central components cause orbital precession [4].
14. Strong nuclear force is approximately:
- A) Non-central
- B) Central
- C) Velocity dependent
- D) Both A and C
Answer: B. Acts radially between nucleons (central at low energies) [5].
15. Central force motion has how many constants of motion?
- A) 1 (energy)
- B) 2 (energy, angular momentum)
- C) 3 (energy, L, direction)
- D) 6
Answer: B. Energy and angular momentum magnitude conserved [2].
16. Which statement is true for central forces?
- A) Always attractive
- B) Always produce circular orbits
- C) Produce no torque
- D) Velocity dependent
Answer: C. Central forces aligned with position vector produce zero torque [1].
17. Foucault pendulum demonstrates:
- A) Central force motion
- B) Earth's rotation (Coriolis - non-central)
- C) Gravitational central force
- D) Magnetic effects
Answer: B. Coriolis force (non-central) causes plane of oscillation to rotate [4].
18. In central force problems, effective potential includes:
- A) V(r) + L²/(2mr²)
- B) V(r) only
- C) Kinetic energy only
- D) Time-dependent term
Answer: A. V_eff(r) = V(r) + L²/(2mr²) governs radial motion [2].
19. Which force violates central force condition?
- A) Tension (along string)
- B) Air resistance (opposite velocity)
- C) Hooke's law F = -kx
- D) Inverse square force
Answer: B. Drag force opposes velocity direction, not radial [3].
20. Stability of planetary orbits requires:
- A) Non-central perturbation forces
- B) Purely central gravitational force
- C) Magnetic field alignment
- D) Constant velocity forces
Answer: B. Kepler's laws follow from central inverse-square gravitational force [1].
