G Variation Altitude

8 MCQs3 revision cards9-step worked example

Source: NCERT GravitationPYQ coverage: NEET 2021, 2022, 2023, 2024, 2025Official key: NTA-verifiedLast reviewed: May 2026

Lesson

The trap that costs marks: You see "find g at height h = R above the surface" and instinctively write g_h = g(1 − 2h/R). That gives g(1 − 2) = −g — a negative acceleration due to gravity. The answer is obviously wrong, but under exam pressure, students pick the distractor built from exactly this mistake. This trap has appeared in NEET 2024 and 2025.

The actual formula. Gravitational acceleration at altitude h above a spherical Earth of radius R is:

g_h = g × (R / (R + h))²

This is an inverse-square dependence on the distance from Earth's centre, not a linear decrease from the surface. The derivation is direct: at the surface, g = GM/R²; at height h, the distance from the centre is (R + h), so g_h = GM/(R + h)² = g × R²/(R + h)² (NCERT Class 11 Physics Chapter 7, page 6).

When does the approximation work? The linear form g_h ≈ g(1 − 2h/R) is a binomial expansion valid only when h ≪ R. For a satellite 200 km above Earth (R ≈ 6400 km), h/R ≈ 0.03 — the approximation is fine. For h = R/2, h = R, or h = 2R, it fails badly.

Quick checkpoint: at h = R, the exact formula gives g_h = g(R/2R)² = g/4. The linear approximation gives g(1 − 2) = −g. If your answer is negative, you used the wrong formula.

Watch-out for NEET stems: Questions often state height as a fraction of R (e.g., "at a height equal to half the radius"). Convert to h = R/2 and substitute into the exact formula. Do not default to the approximation unless the problem explicitly states h ≪ R.

Practice MCQs

Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.

MCQ 1Easy RecallPractice

The acceleration due to gravity at a height h above the Earth's surface is given by which expression? (R = radius of Earth, g = surface gravity)

MCQ 2Easy RecallPractice

The approximate formula g_h ≈ g(1 − 2h/R) for variation of g with altitude is valid under which condition?

MCQ 3Easy RecallPractice

At what altitude above the Earth's surface does the acceleration due to gravity become zero, according to g_h = g(R/(R + h))²?

MCQ 4Direct ApplicationPractice

A body weighs 63 N on the surface of the Earth. What is its weight at a height equal to half the radius of the Earth above the surface?

MCQ 5Direct ApplicationPractice

The acceleration due to gravity at a height of 3200 km above the Earth's surface is (take R = 6400 km, g = 9.8 m/s²):

MCQ 6Direct ApplicationPractice

At what height above the Earth's surface does the acceleration due to gravity reduce to 1/9 of its surface value? (R = radius of Earth)

MCQ 7CalculationPractice

A body weighs W on the surface of the Earth. At what height above the surface will its weight become W/16? Express your answer in terms of R (radius of Earth).

MCQ 8CalculationPractice

The ratio of acceleration due to gravity at a height R above the Earth's surface to that at a depth R/2 below the Earth's surface is: (R = radius of Earth, assume uniform density)

Quick recall before you leave

Worked Example

1
Given
A body weighs 900 N on the surface of the Earth. Find its weight at a height equal to the radius of the Earth (h = R) above the surface. Take R = 6400 km.
2
Required
Weight at height h = R.
3
Concept
Gravitational acceleration decreases with altitude as an inverse-square function of the distance from Earth's centre (NCERT Class 11 Physics Chapter 7, page 6). Weight is proportional to local g.
4
Formula
g_h = g × (R / (R + h))² W_h = W × (R / (R + h))²
5
Substitution
h = R, so (R + h) = 2R. W_h = 900 × (R / 2R)² W_h = 900 × (1/2)²
6
Calculation
W_h = 900 × 1/4 = 225 N Note: the factor 4 in the denominator is an exact counting integer (2² = 4) and does not affect significant-figure count.
7
Final answer
W_h = 225 N The exact constant 4 (from 2² in the denominator) and the integer ratio R/2R = 1/2 do not limit significant figures. The precision is governed by the given weight (900 N, which we treat as exact for this problem since it is a clean given value).
8
Common trap
Using the linear approximation g(1 − 2h/R) here gives g(1 − 2) = −g, implying negative weight. This is the high-frequency trap for this topic — the approximation requires h ≪ R, and h = R violates that condition completely.
9
Similar NEET-style question
A satellite orbits at a height equal to 3 times the radius of the Earth. What fraction of the surface gravity does it experience? (Answer: g_h = g(R/4R)² = g/16.) ---

Before solving, remember these

Formula

Variation of g with altitude

At height h above Earth's surface: g_h = g (R/(R+h))² ≈ g(1 - 2h/R) for h << R. Decreases with altitude.

-- NCERT Class 11 Physics, Ch. 7, p. 6

Formulas

8 formulas — click to collapse

Escape velocity from a body's surface

v_{e} = \frac{2 GM}{R} = 2 g R

Minimum speed for an object to escape gravity to infinity from radius R. Earth: ~11.2 km/s.

Symbol	Quantity	SI Unit
v_e	escape velocity	m/s
M	planet mass	kg
R	planet radius	m
g	surface gravity	m/s^2

Valid when

Launched from surface
No air drag
Body treated as point/sphere

Gravitational potential energy (point masses)

U = - \frac{GM m}{r}

PE of two-body system; negative because gravity is attractive (work to separate them is positive).

Symbol	Quantity	SI Unit
U	grav PE	J
M, m	two masses	kg
r	separation	m

Valid when

Reference U=0 at r=infinity
Point or spherical masses

g variation with altitude

g_{h} = g (\frac{R}{R + h})^{2} \approx g (1 - 2 h / R)

Gravitational acceleration decreases with altitude above Earth's surface.

Symbol	Quantity	SI Unit
g_h	g at height h	m/s^2
g	surface g	m/s^2
R	Earth radius	m
h	altitude	m

Valid when

Static observer at altitude
Earth treated as uniform sphere

g variation with depth

g_{d} = g (1 - d / R)

Inside Earth (uniform density), g decreases linearly with depth, vanishing at centre.

Symbol	Quantity	SI Unit
g_d	g at depth	m/s^2
g	surface g	m/s^2
R	Earth radius	m
d	depth	m

Valid when

Earth treated as uniform density sphere

Kepler's third law

T^{2} = \frac{4 π ^{2}}{GM} a^{3}

Square of orbital period proportional to cube of semi-major axis. Holds for elliptic orbits about a central mass.

Symbol	Quantity	SI Unit
T	orbital period	s
a	semi-major axis	m
M	central mass	kg

Valid when

Two-body system with central mass M >> orbiting mass
Bound orbit

Orbital velocity for circular orbit

v = \frac{GM}{R + h}

Speed of circular orbit at altitude h above body of mass M, radius R.

Symbol	Quantity	SI Unit
v	orbital speed	m/s
M	central mass	kg
R+h	orbit radius	m

Valid when

Circular orbit
M >> orbiting mass

Satellite total mechanical energy

E = - \frac{GM m}{2 ( R + h )}

Total energy = KE + PE = -KE (virial). Always negative for bound orbit; E -> 0 at infinity.

Symbol	Quantity	SI Unit
E	total energy	J
M, m	central mass and satellite mass	kg
R+h	orbit radius	m

Valid when

Circular orbit
Bound (E < 0)

Newton's law of gravitation

F = \frac{G m _{1} m _{2}}{r ^{2}}

Attractive force between any two masses. Inverse-square central force.

Symbol	Quantity	SI Unit
F	force	N
G	grav constant = 6.674e-11	N*m^2/kg^2
m1, m2	masses	kg
r	centre-to-centre distance	m

Valid when

Point masses or spherically symmetric distributions
r > sum of body radii (else use shell theorem)

Exam Traps & Common Mistakes

These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.

4 items — click to collapse

Trap

g at altitude: linear vs inverse-square

Category: Similar Terms

Student treats g(h) as linear in h. Actual: g(R/(R+h))² (inverse-square).

When it triggers

Question asks for g at significant altitude (e.g. R/2 above surface).

How to avoid

Use g_h = g (R/(R+h))². Linear approximation g(1 - 2h/R) only valid for h << R.

Trap

Kepler's third law: linear vs 3/2 power

Category: Similar Terms

Student treats T proportional to a (linear) instead of a^(3/2).

When it triggers

Question gives change in semi-major axis and asks for new period.

How to avoid

T² ∝ a³, so T ∝ a^(3/2). Doubling a multiplies T by 2^(3/2) ≈ 2.83.

Mistake

Treats g(h) as linear in h for significant heights.

Root cause: formula misuse

Correction

Use g_h = g(R/(R+h))² (inverse-square). Linear approximation g(1-2h/R) is only valid for h << R. For h = R/2, the exact formula gives g_h = (2/3)² g = 4g/9, not g(1-1) = 0.

Mistake

Treats T proportional to a (linear) instead of a^(3/2) in Kepler's third law.

Root cause: formula misuse

Correction

T² ∝ a³, so T ∝ a^(3/2). Doubling a multiplies T by 2^(3/2) ≈ 2.83. Quadrupling a → 8× T.

Past Year Questions

8 questions from NEET 2021, 2022, 2023, 2024, 2025. Answers verified against NTA official keys. — click to collapse

NEET 2025

The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?

1124 earth days

288 earth days

3225 earth days

4172 earth days

NTA Answer: Option 2(final)

NEET 2025

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is :

136 N

216 N

327 N

432 N

NTA Answer: Option 3(final)

NEET 2024Revised key

1 The mass of a planet is th that of the earth and its diameter is half that of the earth. The acceleration due 10 to gravity on that planet is:

119.6 m s–2

29.8 m s–2

34.9 m s–2

43.92 m s–2

NTA Answer: Option 4(revised_final)

NEET 2024Revised key

The minimum energy required to launch a satellite of mass m from the surface of earth of mass M and radius R in a circular orbit at an altitude of 2R from the surface of the earth is: 5GmM

16R 2GmM

23R GmM

32R GmM

43R

NTA Answer: Option 1(revised_final)

NEET 2023

Two bodies of mass m and 9m are placed at a distance R. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (G = gravitational constant) 12Gm 16Gm

1−

2− R R 20Gm 8Gm

3−

4− R R

NTA Answer: Option 2(final)

NEET 2023

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is 3π the universal constant of gravitation, the quantity represents Gd

1T2

2T3

NTA Answer: Option 1(final)

NEET 2022

A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is

1180 N/kg

20.05 N/kg

350 N/kg

420 N/kg

NTA Answer: Option 3(final)

NEET 2021

The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is

14v

32v

43v

NTA Answer: Option 1(final)

How NEET usually asks this

4 recurring patterns from past papers — click to collapse

Compare escape velocities for planets with different M, R. v_e ∝ sqrt(M/R). Common shape: 'planet has 4× radius and 2× density of Earth — find v_e'.

Direct ApplicationEasy

Common distractors

forgets density not mass

Confuses planet mass with density given radius scaling

Body weighs W on surface; find weight at height h above surface. Use g_h = g(R/(R+h))^2.

Direct ApplicationEasy

Common distractors

uses linear decrease with h

Treats g as linear in h instead of inverse-square

Given period T and semi-major axis a of one planet, find for another with different a. T^2 ∝ a^3.

Direct ApplicationEasy

Common distractors

uses linear relation

Treats T proportional to a not a^(3/2)

Energy required to launch satellite to altitude. Compute change in total mechanical energy.

Multi StepMedium

Common distractors

forgets orbital KE component

Computes only PE change, ignoring orbital KE

Sources

NCERT refs: Class 11 Physics Chapter 7, p.6

Test yourself on this topic with real past-paper questions:

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Escape Velocity G Variation Depth

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G Variation Altitude

Lesson

Practice MCQs

Quick recall before you leave

g_h = g(R/(R + h))²

g_h ≈ g(1 − 2h/R)

g_d = g(1 − d/R)

Worked Example

Before solving, remember these

Formulas

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Exam Traps & Common Mistakes

When it triggers

How to avoid

When it triggers

How to avoid

Correction

Correction

Past Year Questions

How NEET usually asks this

Common distractors

Common distractors

Common distractors

Common distractors

Sources

Free NEET study resources