Escape Velocity

8 MCQs3 revision cards9-step worked example

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

Lesson

Escape velocity is the minimum launch speed needed for an object to leave a planet's gravitational field permanently — reaching infinity with zero residual speed. The derivation is energy conservation: set total mechanical energy at launch equal to zero (the boundary between bound and unbound trajectories).

At the surface, KE + PE = 0 gives ½mv² + (−GMm/R) = 0, yielding v_e = √(2GM/R). Since g = GM/R², this simplifies to v_e = √(2gR). For Earth, v_e ≈ 11.2 km/s (NCERT Class 11 Physics Chapter 7, page 10).

Key features you must internalise:

Independent of the launched object's mass. The m cancels. A marble and a rocket have the same escape velocity from a given planet.
Independent of launch direction. The derivation uses energy (scalar), not force components. Horizontal, vertical, or at 45° — the threshold speed is identical.
Depends only on M and R of the planet (or equivalently, g and R). This is the basis of every NEET scaling question.

The high-frequency NEET pattern asks you to compare escape velocities when a planet's radius, mass, or density changes relative to Earth. The relationship v_e = √(2GM/R) can be rewritten using M = (4/3)πR³ρ as v_e = R√(8πGρ/3). This density form is what examiners exploit: when density is given instead of mass, students who substitute M directly get the wrong scaling.

Watch-out: forgetting to convert density-radius data into mass before applying v_e ∝ √(M/R) leads to a common distractor. Always decide first: am I given M directly, or must I express M in terms of ρ and 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 escape velocity from the surface of a planet depends on:

MCQ 2Easy RecallPractice

The escape velocity from the surface of the Earth is approximately:

MCQ 3Easy RecallPractice

The escape velocity from a planet's surface is related to the orbital velocity of a satellite in a near-surface orbit by:

MCQ 4Direct ApplicationPractice

A planet has mass 4M and radius 2R, where M and R are Earth's mass and radius respectively. The escape velocity from this planet's surface, in terms of Earth's escape velocity v_e, is:

MCQ 5Direct ApplicationPYQ Pattern

A planet has 4 times the radius and the same average density as Earth. The ratio of escape velocity from this planet to that from Earth is:

MCQ 6Direct ApplicationPractice

If the mass of Earth were doubled and its radius halved, the new escape velocity would be:

MCQ 7Concept TrapPractice

An object is launched from a planet's surface at exactly the escape velocity. Which statement about its journey is correct?

MCQ 8CalculationPractice

A planet has radius R and surface gravitational acceleration g. A body is projected vertically upward from the surface with speed v = v_e / 2, where v_e is the escape velocity. The maximum height reached by the body above the surface is:

Quick recall before you leave

Worked Example

Pattern: Escape velocity scaling when planet parameters change (NEET pattern: escape velocity scaling, PYQ 2021)

1
Given
- Planet radius: R' = 4R_E - Planet density: ρ' = 2ρ_E - Earth escape velocity: v_e (known)
2
Required
Escape velocity from the planet's surface, expressed as a multiple of v_e.
3
Concept
Escape velocity depends on mass and radius: v_e = √(2GM/R). When density is given, substitute M = (4/3)πR³ρ to get the density form: v_e = R√(8πGρ/3). This reveals v_e ∝ R√ρ.
4
Formula
v_e = R√(8πGρ/3), so v_e ∝ R√ρ
5
Substitution
v_e(planet) / v_e(Earth) = (R' × √ρ') / (R_E × √ρ_E) = (4R_E × √(2ρ_E)) / (R_E × √ρ_E)
6
Calculation
= 4 × √2 = 4√2 Note: The factors 4 (radius ratio) and 2 (density ratio) are exact problem-defined integers. They do not limit significant figures. The constants 8, π, G, and 3 in the formula are mathematical/physical constants and are also exact for this ratio calculation.
7
Final answer
v_e(planet) = 4√2 × v_e ≈ 5.66 × v_e
8
Common trap
**Forgetting to convert density to mass.** If a student directly uses v_e ∝ √(M/R) without computing M = (4/3)π(4R)³(2ρ) = 128 × (4/3)πR³ρ = 128M_E, they may apply the wrong scaling. The density form v_e ∝ R√ρ avoids this error.
9
Similar NEET-style question
A planet has 3 times the radius and 3 times the average density of Earth. What is the escape velocity from this planet, given that Earth's escape velocity is 11.2 km/s? *Approach:* v_e ∝ R√ρ → ratio = 3 × √3 = 3√3 ≈ 5.20. Answer: 5.20 × 11.2 ≈ 58.2 km/s. ---

Before solving, remember these

Formula

Escape velocity

The minimum speed required to escape Earth's gravity: v_e = √(2 G M / R) = √(2 g R) ≈ 11.2 km/s. Independent of the mass of the projectile; depends only on the gravitating body.

-- NCERT Class 11 Physics, Ch. 7, p. 10

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.10

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

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Acceleration Due to Gravity G Variation Altitude

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Escape Velocity

Lesson

Practice MCQs

Quick recall before you leave

Escape velocity formula

Escape velocity — density form

Gravitational PE

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