Here are 20 multiple-choice questions (MCQs) on the inverse square law with explained answers:
1. What does the inverse square law state?
- A) Intensity is directly proportional to distance
- B) Intensity is inversely proportional to distance
- C) Intensity is inversely proportional to square of the distance
- D) Intensity is proportional to square of the distance
Answer: C. Intensity varies inversely as the square of the distance from the source due to spreading over a spherical surface area [1].
2. If the distance from a light source is doubled, the intensity becomes:
- A) Half
- B) One fourth
- C) Twice
- D) Four times
Answer: B. Intensity decreases to 1/4 because intensity ∝ 1/r² [2].
3. Which phenomenon follows the inverse square law?
- A) Gravitational force
- B) Frictional force
- C) Magnetic force between parallel wires
- D) Buoyant force
Answer: A. Gravity follows inverse square law with force ∝ 1/r² [1].
4. The formula $$I \propto \frac{1}{r^2}$$ means:
- A) Intensity is proportional to distance squared
- B) Intensity is inversely proportional to distance squared
- C) Intensity is proportional to distance
- D) Intensity is constant
Answer: B. Intensity decreases with square of distance from the source [2].
5. Coulomb’s law follows inverse square law for:
- A) Force between two charges
- B) Electric potential
- C) Magnetic field strength
- D) None
Answer: A. Force between electric charges follows inverse square of distance [2].
6. What happens to radiation intensity at 3 m if intensity at 1 m is I?
- A) 3I
- B) I/3
- C) I/9
- D) 9I
Answer: C. Intensity at 3 m is $$I/3^2 = I/9$$ [1].
7. Which of the following does not obey inverse square law?
- A) Light intensity
- B) Sound intensity from a point source
- C) Electric field of a point charge
- D) Magnetic force between two current-carrying wires
Answer: D. Magnetic force between wires follows different law, not inverse square [3].
8. The surface area over which energy spreads is proportional to:
- A) r
- B) r²
- C) r³
- D) 1/r²
Answer: B. Sphere surface area is $$4\pi r^2$$, causing intensity to reduce with $$r^2$$ [1].
9. Inverse square law applies to:
- A) Two-dimensional fields
- B) Three-dimensional point sources
- C) One-dimensional sources
- D) None
Answer: B. It applies to 3D radial distribution from a point source [1].
10. What is the intensity if distance from source is halved?
- A) 1/4 original
- B) 4 times original
- C) Half original
- D) Same
Answer: B. Intensity becomes four times because of inverse square relation [2].
11. The gravitational force between two masses is 100 N at a distance of 2 m. What will it be at 1 m?
- A) 25 N
- B) 400 N
- C) 50 N
- D) 100 N
Answer: B. Force quadruples when distance halves, $$100 \times (2/1)^2 = 400$$ N [1].
12. Electric field strength $$E$$ varies with distance as:
- A) $$1/r$$
- B) $$1/r^3$$
- C) $$1/r^2$$
- D) $$r^2$$
Answer: C. Field strength for a point charge follows inverse square law [3].
13. What happens to the flux through a sphere if radius doubles?
- A) Doubles
- B) Quadruples
- C) Halves
- D) Constant
Answer: D. Flux through sphere remains constant; intensity decreases due to area increase [1].
14. Which quantity does not change with distance according to inverse square law?
- A) Force
- B) Intensity
- C) Total energy emitted by the source
- D) Irradiance
Answer: C. Total energy emitted is constant; spreading reduces intensity [1].
15. Why does inverse square law hold true in 3-dimensional space?
- A) Because of linear geometry
- B) Due to constant velocity of propagation
- C) Because surface area of a sphere ∝ $$r^2$$
- D) Because energy increases with distance
Answer: C. Energy spreads over spherical area $$\propto r^2$$, hence intensity $$\propto 1/r^2$$ [1].
16. At 10 m, the intensity is 25 units. What is intensity at 20 m?
- A) 100 units
- B) 12.5 units
- C) 6.25 units
- D) 50 units
Answer: C. Intensity at 20 m is $$25 \times (10/20)^2=25 \times 1/4=6.25$$ units [2].
17. If intensity is 50 W/m² at 5 m, what is intensity at 15 m?
- A) 16.67 W/m²
- B) 5.55 W/m²
- C) 150 W/m²
- D) 10 W/m²
Answer: B. Intensity decreases by factor $$(5/15)^2=1/9$$, so $$50/9 \approx 5.55$$ W/m² [2].
18. What does the inverse square law explain about radiation safety?
- A) Distance doesn't affect exposure
- B) Increasing distance greatly reduces exposure
- C) Exposure rises with distance
- D) None
Answer: B. Increasing distance from a source reduces exposure by square of distance [2].
19. Which is the correct unit for intensity in inverse square law?
- A) Candela (cd)
- B) Meter (m)
- C) Watt per square meter (W/m²)
- D) Joule (J)
Answer: C. Intensity or irradiance unit is Watts/m² [4].
20. The inverse square law can be represented mathematically as:
- A) $$I_1 r_1 = I_2 r_2$$
- B) $$I_1 r_1^2 = I_2 r_2^2$$
- C) $$I_1 r_1^3 = I_2 r_2^3$$
- D) $$I_1 = I_2$$
Answer: B. $$I_1 r_1^2 = I_2 r_2^2$$ shows conservation of intensity relation [1].
