JEE Main - Acceleration due to gravity and its variation Online Test (MCQ Quiz)

1. What is the standard value of acceleration due to gravity at the Earth's surface?

A) 9.8 m/s² B) 1.62 m/s² C) 10.0 m/s² D) 0 m/s²

2. The acceleration due to gravity on the surface of the Earth is approximately:

A) GM/R B) GM/R² C) g/R D) gR

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

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. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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%

38. 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

39. 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

40. 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

41. 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)

42. 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

43. 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

44. 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

45. 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.

46. 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

47. 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

48. 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

49. 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

50. 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

Acceleration due to gravity and its variation - Online Test

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