Acceleration due to gravity and its variation - Question Bank

1. If the Earth were a perfect sphere with no rotation and uniform density, the acceleration due to gravity would be:
A) Constant everywhere on the surface
B) Maximum at the equator
C) Minimum at the poles
D) Zero at the center
2. The apparent weight of a person standing on a weighing machine at the equator is less than their actual weight due to:
A) Centrifugal force
B) Gravitational force
C) Normal reaction force
D) Frictional force
3. The acceleration due to gravity of a body moving inside a uniform spherical Earth of radius R, at a distance r from the center (r < R), is proportional to:
A) r
B) 1/r
C) r²
D) 1/r²
4. The variation of 'g' with altitude is given by g' = GM/(R+h)². For very large heights (h >> R), 'g' approaches:
A) g
B) 0
C) g/h
D) gR/h
5. The gravitational acceleration 'g' at the Earth's surface is approximately 9.8 m/s². What would be the approximate value of 'g' on a planet with twice the radius and twice the mass of Earth?
A) 4.9 m/s²
B) 9.8 m/s²
C) 19.6 m/s²
D) 39.2 m/s²
6. The effect of Earth's rotation on 'g' is most pronounced at:
A) The poles
B) The equator
C) Mid-latitudes
D) Anywhere on the surface equally
7. Which of the following statements about acceleration due to gravity is INCORRECT?
A) It is maximum at the poles.
B) It is minimum at the equator due to rotation.
C) It decreases with altitude.
D) It increases with depth below the surface.
8. The acceleration due to gravity at a distance 'r' from the center of a uniform sphere of radius R and mass M is proportional to:
A) r for r < R and 1/r² for r > R
B) 1/r² for all r
C) r for r < R and r² for r > R
D) 1/r for r < R and 1/r² for r > R
9. If an object is taken from the Earth's surface to a depth 'd', its weight decreases by approximately:
A) (d/R) × 100%
B) (2d/R) × 100%
C) (d²/R²) × 100%
D) Zero
10. The variation of 'g' with latitude is mainly due to:
A) Earth's non-spherical shape and rotation
B) Earth's rotation only
C) Earth's non-spherical shape only
D) Altitude variations
11. The acceleration due to gravity inside a uniform spherical shell of mass M and radius R, at a distance r from the center (r < R), is:
A) GM/r²
B) Zero
C) GM/R²
D) g(r/R)
12. The acceleration due to gravity at a height 'h' from the surface of the Earth is given by g(1 - 2h/R). If h = R, the value of g would be:
A) g/2
B) g/3
C) 0
D) g
13. Why is the value of 'g' slightly less at the equator than at the poles, even if the Earth were a perfect sphere?
A) Higher altitude at the equator
B) Centrifugal force due to rotation
C) Lower mass at the equator
D) Difference in gravitational constant
14. If the Earth's mass were doubled and its radius remained the same, the acceleration due to gravity at the surface would:
A) Halve
B) Double
C) Quadruple
D) Remain the same
15. The acceleration due to gravity at a height 'h' above the surface is g' = GM/(R+h)². The percentage decrease in 'g' for a small height 'h' is approximately:
A) (h/R) × 100%
B) (2h/R) × 100%
C) (h²/R²) × 100%
D) (1/2) × (h/R) × 100%
16. At what depth below the Earth's surface would the acceleration due to gravity be half of that at the surface, assuming uniform density?
A) R/2
B) R
C) 3R/2
D) 0
17. The acceleration due to gravity on the surface of a planet of mass M and radius R is proportional to:
A) M/R
B) M/R²
C) MR
D) M²R
18. The variation of 'g' with depth is significant for:
A) Depths much smaller than Earth's radius
B) Depths comparable to Earth's radius
C) Depths much larger than Earth's radius
D) Only for objects on the surface
19. The variation of 'g' with altitude is significant for:
A) Heights much smaller than Earth's radius
B) Heights comparable to Earth's radius
C) Heights much larger than Earth's radius
D) Only for objects on the surface
20. If the Earth stops rotating, the acceleration due to gravity at the equator would:
A) Increase
B) Decrease
C) Remain the same
D) Become zero
21. The effective acceleration due to gravity decreases with latitude due to:
A) Centrifugal force and polar bulge
B) Centrifugal force and equatorial bulge
C) Centrifugal force only
D) Bulge effect only
22. The term 'apparent weight' refers to the weight measured by:
A) A spring balance in free space
B) A spring balance in an accelerating frame
C) A simple balance scale
D) A gravitational field
23. If a body is taken from the Earth's surface to a great height, its weight will:
A) Increase
B) Decrease
C) Remain unchanged
D) Become zero
24. What is the approximate value of acceleration due to gravity on the Moon's surface?
A) 9.8 m/s²
B) 1.62 m/s²
C) 3.7 m/s²
D) 24.5 m/s²
25. An object weighs less at the equator than at the poles. This is mainly because:
A) The Earth is not a perfect sphere
B) The distance from the center is greater at the equator
C) The centrifugal force due to rotation is maximum at the equator
D) The gravitational pull is weaker at the equator
26. The acceleration due to gravity decreases with altitude because:
A) The mass of the Earth effectively decreases
B) The distance from the Earth's center increases
C) The gravitational constant decreases
D) The Earth's rotation slows down
27. If the Earth's radius were halved, keeping its mass constant, the acceleration due to gravity at the surface would:
A) Halve
B) Double
C) Quadruple
D) Remain the same
28. The mass of the Earth is approximately 6 × 10^24 kg and its radius is approximately 6.4 × 10^6 m. The value of G is 6.67 × 10^-11 Nm²/kg². Calculate the approximate value of g at the surface.
A) 9.8 m/s²
B) 16.2 m/s²
C) 1.62 m/s²
D) 0.98 m/s²
29. The value of acceleration due to gravity is highest at:
A) The equator
B) The North Pole
C) The South Pole
D) A point 45° latitude
30. If the Earth had a uniform density, the acceleration due to gravity at a depth 'd' would be proportional to:
A) d
B) 1/d
C) d²
D) 1/d²
31. When we consider the variation of 'g' with altitude, the formula g' = GM/(R+h)² is exact. The approximate formula g' ≈ g(1 - 2h/R) is valid when:
A) h is very large compared to R
B) h is comparable to R
C) h is very small compared to R
D) h is equal to R
32. Consider a point mass 'm' at a height 'h' from the Earth's surface. The gravitational force is proportional to 1/r², where 'r' is the distance from the center. How does 'g' vary with 'r'?
A) g ∝ r
B) g ∝ 1/r
C) g ∝ r²
D) g ∝ 1/r²
33. The effective acceleration due to gravity at the equator (λ=0°) is given by g_eff = g - Rω². This shows that:
A) Gravity is maximum at the equator
B) Rotation reduces gravity at the equator
C) Rotation increases gravity at the equator
D) Rotation has no effect at the equator
34. The effective acceleration due to gravity at a latitude 'λ' is given by g_eff = g - Rω²cos²λ, where 'g' is the gravity without rotation and 'ω' is the angular velocity of Earth. What is the effective acceleration at the poles (λ=90°)?
A) g
B) g - Rω²
C) g + Rω²
D) 0
35. If a tunnel is dug from one side of the Earth to the other passing through the center, the acceleration due to gravity of an object inside the tunnel will be:
A) Maximum at the center
B) Minimum at the center
C) Zero at the center
D) Constant throughout
36. A satellite orbits the Earth at a certain height. If the height increases, the acceleration due to gravity experienced by the satellite:
A) Increases
B) Decreases
C) Remains the same
D) Becomes zero
37. Which factor contributes the least to the variation of 'g' across the Earth's surface?
A) Altitude
B) Latitude
C) Earth's rotation
D) Local geological variations in density
38. The flattening of the Earth at the poles and bulging at the equator causes 'g' to be:
A) Greater at the equator than at the poles
B) Lesser at the equator than at the poles
C) Equal at the equator and poles
D) Zero at the poles
39. If the Earth's density were not uniform, how would that affect the variation of 'g' with depth?
A) The variation would still be linear
B) The variation would not be linear
C) The value of 'g' at the center would increase
D) The value of 'g' at the surface would decrease
40. What is the acceleration due to gravity at the center of the Earth, assuming uniform density?
A) g
B) g/2
C) 0
D) Infinite
41. The formula for acceleration due to gravity at a depth 'd' below the Earth's surface is approximately g'' = g(1 - d/R) for:
A) Any depth d
B) d << R
C) d >> R
D) d = R
42. How does the acceleration due to gravity change with depth below the Earth's surface (assuming uniform density)?
A) It increases linearly
B) It decreases linearly
C) It remains constant
D) It decreases inversely with the square of the depth
43. The decrease in acceleration due to gravity at the equator compared to the poles is primarily due to:
A) Earth's non-spherical shape
B) Centrifugal force due to rotation
C) Higher altitude at the equator
D) Lower mass of the Earth at the equator
44. At which location on Earth's surface is the apparent acceleration due to gravity the maximum?
A) Equator
B) Poles
C) Mid-latitudes
D) Sea level
45. What is the effect of Earth's rotation on the apparent acceleration due to gravity?
A) It increases gravity at the equator
B) It decreases gravity at the equator
C) It has no effect on gravity
D) It increases gravity at the poles
46. The formula for acceleration due to gravity at a height 'h' above the Earth's surface is approximately g' = g(1 - 2h/R) for:
A) Any height h
B) h << R
C) h >> R
D) h = R
47. How does the acceleration due to gravity change as you move away from the Earth's center (altitude increases)?
A) It increases linearly
B) It decreases linearly
C) It decreases inversely with the square of the distance
D) It increases inversely with the square of the distance
48. What is the primary reason for the variation of acceleration due to gravity with altitude?
A) Change in Earth's mass
B) Change in distance from the Earth's center
C) Change in Earth's rotation speed
D) Change in gravitational constant
49. If the Earth were to shrink, keeping its mass constant, how would the acceleration due to gravity at its surface change?
A) Increase
B) Decrease
C) Remain the same
D) Become zero
50. The acceleration due to gravity on the surface of the Earth is approximately:
A) GM/R
B) GM/R²
C) g/R
D) gR