Grav Potential

8 MCQs2 revision cards9-step worked example

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

Lesson

Gravitational potential is where sign errors silently cost you marks. The concept itself is straightforward, but NEET questions exploit the negative sign and the distinction between potential (a scalar field property) and potential energy (a system property).

Gravitational potential at a point is the work done per unit mass by an external agent in bringing a test mass from infinity to that point, against the gravitational field. For a point mass M at distance r (NCERT Class 11 Physics Chapter 7, page 8):

V = −GM/r

The negative sign is not a convention you can drop — it encodes that gravity is attractive. At infinity, V = 0 (the reference). As you approach the mass, V becomes more negative: the field does positive work on an inward-moving object, so an external agent does negative work.

Potential vs. potential energy. Gravitational potential V is a property of the field at a point (unit: J/kg). Gravitational potential energy U = mV = −GMm/r is a property of the two-body system (unit: J). Confusing the two — especially dropping the test mass m or misapplying the sign — is a common source of wrong answers.

Superposition. Gravitational potential is a scalar. For multiple masses, add potentials algebraically: V_total = V₁ + V₂ + … No vector resolution needed. This makes potential calculations simpler than force calculations in multi-body problems.

Key watch-out: When a question says "gravitational potential at the surface of Earth," the answer is V = −GM/R (negative). If you write +GM/R, you have the wrong sign and will pick a distractor. The magnitude alone is not the potential.

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 SI unit of gravitational potential is:

MCQ 2Easy RecallPractice

The gravitational potential at a point infinitely far from an isolated mass M is:

MCQ 3Easy RecallPractice

Gravitational potential is a scalar quantity. When computing the net gravitational potential at a point due to multiple masses, you:

MCQ 4Direct ApplicationPractice

The gravitational potential at the surface of Earth is V. What is the gravitational potential energy of a body of mass m placed on the surface?

MCQ 5Direct ApplicationPractice

Two point masses, each of mass M, are placed a distance 2d apart. The gravitational potential at the midpoint of the line joining them is:

MCQ 6Direct ApplicationPractice

A particle is moved from the surface of a planet (radius R, mass M) to a height R above the surface. The change in gravitational potential is:

MCQ 7Concept TrapPractice

At the midpoint between two equal point masses, the gravitational field is zero but the gravitational potential is not zero. This is because:

MCQ 8CalculationPractice

A uniform sphere of mass M and radius R has gravitational potential V₁ at its surface and V₂ at a distance 3R from its centre. The ratio V₁/V₂ is:

Quick recall before you leave

Worked Example

1
Given
- Planet mass: M, radius: R (both exact problem-defined symbols) - Body mass: m - Initial position: surface (r₁ = R from centre) - Final position: height 2R above surface (r₂ = R + 2R = 3R from centre)
2
Required
Work done by external agent, W_ext
3
Concept
Work done by an external agent against gravity equals the change in gravitational potential energy of the system: W_ext = ΔU = U_final − U_initial. This uses the gravitational PE formula U = −GMm/r (NCERT Class 11 Physics Chapter 7, page 8).
4
Formula
U = −GMm/r W_ext = U_final − U_initial = (−GMm/r₂) − (−GMm/r₁)
5
Substitution
W_ext = (−GMm/(3R)) − (−GMm/R)
6
Calculation
W_ext = −GMm/(3R) + GMm/R W_ext = GMm/R × (−1/3 + 1) W_ext = GMm/R × (2/3) W_ext = 2GMm/(3R) Note: M, m, R are exact problem-defined quantities; the integers 2 and 3 are exact counting numbers. Neither constrains significant figures.
7
Final answer
W_ext = 2GMm/(3R) The work is positive, confirming that the external agent must do work against gravity to move the body outward.
8
Common trap
A common confusion is computing only the change in potential (ΔV) and forgetting to multiply by the body's mass m. ΔV = GM/(3R) − (−GM/R) would give a J/kg quantity, not the J required. Always use ΔU = mΔV for the actual work/energy. Another error: using the height (2R) as the final distance from the centre instead of the total distance (R + 2R = 3R). The formula U = −GMm/r requires the distance from the planet's centre, not from the surface.
9
Similar NEET-style question
A satellite of mass m is to be placed in orbit at height R above a planet of mass M, radius R. What minimum energy must be supplied to move it from the surface to that height? (Ignore orbital KE — only consider the change in gravitational PE.) ---

Before solving, remember these

Formula

Gravitational potential energy

U = -G M m / r (taking U → 0 as r → ∞). Negative sign reflects that gravity is attractive — work must be done against it to separate masses. For two-body system at separation r.

-- NCERT Class 11 Physics, Ch. 7, p. 8

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.8

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

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Grav Potential

Lesson

Practice MCQs

Quick recall before you leave

Gravitational potential (point mass)

Gravitational potential energy (two-body)

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