Acceleration due to gravity and its variation - One Line Questions
1.
If an object is taken from the Earth's surface to a depth 'd', its weight decreases by approximately: —
(d/R) × 100%
2.
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: —
(2h/R) × 100%
3.
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? —
9.8 m/s²
4.
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. —
9.8 m/s²
5.
What is the approximate value of acceleration due to gravity on the Moon's surface? —
1.62 m/s²
6.
What is the standard value of acceleration due to gravity at the Earth's surface? —
9.8 m/s²
7.
The term 'apparent weight' refers to the weight measured by: —
A spring balance in an accelerating frame
8.
Which factor contributes the least to the variation of 'g' across the Earth's surface? —
Altitude
9.
The formula for acceleration due to gravity at a depth 'd' below the Earth's surface is approximately g'' = g(1 - d/R) for: —
d << R
10.
The formula for acceleration due to gravity at a height 'h' above the Earth's surface is approximately g' = g(1 - 2h/R) for: —
h << R
11.
The apparent weight of a person standing on a weighing machine at the equator is less than their actual weight due to: —
Centrifugal force
12.
The effective acceleration due to gravity decreases with latitude due to: —
Centrifugal force and equatorial bulge
13.
What is the primary reason for the variation of acceleration due to gravity with altitude? —
Change in distance from the Earth's center
14.
If the Earth were a perfect sphere with no rotation and uniform density, the acceleration due to gravity would be: —
Constant everywhere on the surface
15.
If the Earth had a uniform density, the acceleration due to gravity at a depth 'd' would be proportional to: —
d
16.
The variation of 'g' with depth is significant for: —
Depths comparable to Earth's radius
17.
The decrease in acceleration due to gravity at the equator compared to the poles is primarily due to: —
Centrifugal force due to rotation
18.
The variation of 'g' with latitude is mainly due to: —
Earth's non-spherical shape and rotation
19.
At which location on Earth's surface is the apparent acceleration due to gravity the maximum? —
Poles
20.
The variation of 'g' with altitude is given by g' = GM/(R+h)². For very large heights (h >> R), 'g' approaches: —
0
21.
What is the acceleration due to gravity at the center of the Earth, assuming uniform density? —
0
22.
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°)? —
g
23.
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'? —
g ∝ 1/r²
24.
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: —
g/3
25.
The acceleration due to gravity on the surface of the Earth is approximately: —
GM/R²
26.
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: —
Zero
27.
The effective acceleration due to gravity at the equator (λ=0°) is given by g_eff = g - Rω². This shows that: —
Rotation reduces gravity at the equator
28.
The flattening of the Earth at the poles and bulging at the equator causes 'g' to be: —
Lesser at the equator than at the poles
29.
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: —
h is very small compared to R
30.
If the Earth's radius were halved, keeping its mass constant, the acceleration due to gravity at the surface would: —
Quadruple
31.
If the Earth's mass were doubled and its radius remained the same, the acceleration due to gravity at the surface would: —
Double
32.
The variation of 'g' with altitude is significant for: —
Heights comparable to Earth's radius
33.
Why is the value of 'g' slightly less at the equator than at the poles, even if the Earth were a perfect sphere? —
Centrifugal force due to rotation
34.
If a body is taken from the Earth's surface to a great height, its weight will: —
Decrease
35.
If the Earth stops rotating, the acceleration due to gravity at the equator would: —
Increase
36.
If the Earth were to shrink, keeping its mass constant, how would the acceleration due to gravity at its surface change? —
Increase
37.
A satellite orbits the Earth at a certain height. If the height increases, the acceleration due to gravity experienced by the satellite: —
Decreases
38.
What is the effect of Earth's rotation on the apparent acceleration due to gravity? —
It decreases gravity at the equator
39.
How does the acceleration due to gravity change as you move away from the Earth's center (altitude increases)? —
It decreases inversely with the square of the distance
40.
How does the acceleration due to gravity change with depth below the Earth's surface (assuming uniform density)? —
It decreases linearly
41.
Which of the following statements about acceleration due to gravity is INCORRECT? —
It increases with depth below the surface.
42.
The acceleration due to gravity on the surface of a planet of mass M and radius R is proportional to: —
M/R²
43.
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: —
Zero at the center
44.
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: —
r
45.
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: —
r for r < R and 1/r² for r > R
46.
At what depth below the Earth's surface would the acceleration due to gravity be half of that at the surface, assuming uniform density? —
R/2
47.
An object weighs less at the equator than at the poles. This is mainly because: —
The centrifugal force due to rotation is maximum at the equator
48.
The value of acceleration due to gravity is highest at: —
The North Pole
49.
The acceleration due to gravity decreases with altitude because: —
The distance from the Earth's center increases
50.
The effect of Earth's rotation on 'g' is most pronounced at: —
The equator