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. 135Gravitational Potential
8 MCQs4 revision cards9-step worked example
Source: NCERT GravitationPYQ coverage: NEET 2023Official key: NTA-verifiedLast updated: 25 Sep 2026
Gravitational Potential, explained for NEET
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 135):
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.
Can you answer these Gravitational Potential 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:
Show answer and why every option is right or wrong
Answer: B. Gravitational potential is work done per unit mass, so its unit is J/kg. (NCERT Class 11 Physics Chapter 7, page 135.)
Why A is wrong: A: J is the unit of energy (or potential energy U = mV), not potential V. Confusing potential with potential energy is the root error.
Why C is wrong: C: N/kg is dimensionally equivalent to m/s² (the unit of gravitational field strength or acceleration), not J/kg. While gravitational field g = −dV/dr, the field and the potential have different units.
Why D is wrong: D: J·kg has dimensions of energy × mass, which does not correspond to any standard gravitational quantity.
MCQ 2Easy RecallPractice
The gravitational potential at a point infinitely far from an isolated mass M is:
Show answer and why every option is right or wrong
Answer: C. By the standard convention, gravitational potential is defined with V = 0 at r → ∞. (NCERT Class 11 Physics Chapter 7, page 135.)
Why A is wrong: A: −GM is dimensionally incorrect for potential (missing 1/r), and the reference point at infinity is zero by definition.
Why B is wrong: B: +GM is dimensionally incorrect and also misplaces the sign.
Why D is wrong: D: V → −∞ would apply as r → 0 (approaching the point mass), not at r → ∞.
MCQ 3Easy RecallPractice
Gravitational potential is a scalar quantity. When computing the net gravitational potential at a point due to multiple masses, you:
Show answer and why every option is right or wrong
Answer: A. Since gravitational potential is a scalar with a sign (always negative for attractive masses), the net potential is the algebraic sum V_total = V₁ + V₂ + … including the negative signs. (NCERT Class 11 Physics Chapter 7, page 135.)
Why B is wrong: B: Adding magnitudes discards the negative signs. Since all individual potentials are negative, the magnitude sum would give a positive number — the opposite of the correct (negative) result.
Why C is wrong: C: There are no 'potential vectors' — potential is a scalar, not a vector. Vector addition applies to gravitational force or field, not potential.
Why D is wrong: D: Superposition requires summing all contributions. Ignoring smaller potentials gives an incorrect result.
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?
Show answer and why every option is right or wrong
Answer: B. Gravitational potential energy U = mV, by definition of V as work per unit mass. (NCERT Class 11 Physics Chapter 7, page 135.)
Why A is wrong: A: V/m inverts the relationship. Potential = PE per unit mass (V = U/m), so U = mV, not V/m.
Why C is wrong: C: m/V has no physical meaning in this context and dimensionally yields kg²/J.
Why D is wrong: D: −mV introduces a spurious extra negative sign. V is already negative (V = −GM/R), so U = mV is automatically negative. Writing −mV would make U positive, which is wrong for a bound gravitational system.
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:
Show answer and why every option is right or wrong
Answer: A. The midpoint is at distance d from each mass. Potential due to each: V₁ = V₂ = −GM/d. Since potential is a scalar, V_total = −GM/d + (−GM/d) = −2GM/d. (NCERT Class 11 Physics Chapter 7, page 135.)
Why B is wrong: B: −GM/d accounts for only one of the two masses. Both contribute equally at the midpoint, so you must add both.
Why C is wrong: C: Zero would be correct if potentials were vectors that cancel by symmetry (like the gravitational field at the midpoint). But potential is a scalar — both contributions are negative and add to a more negative value, not zero. This is a high-frequency confusion between field (vector, cancels at midpoint) and potential (scalar, adds).
Why D is wrong: D: −GM/2d incorrectly uses the total separation 2d instead of the distance from the midpoint to each mass, which is d.
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:
Show answer and why every option is right or wrong
Answer: C. V_surface = −GM/R. At height R, distance from centre = 2R, so V_h = −GM/(2R). Change ΔV = V_h − V_surface = −GM/(2R) − (−GM/R) = −GM/(2R) + GM/R = +GM/(2R). The potential increases (becomes less negative) as you move away from the mass. (NCERT Class 11 Physics Chapter 7, page 135.)
Why A is wrong: A: +GM/R would be the change if V went from −GM/R to zero (i.e., moved to infinity). At height R the particle is at r = 2R, not infinity, so the change is smaller.
Why B is wrong: B: −GM/(2R) has the wrong sign. Moving away from a mass makes the potential less negative (increase), not more negative (decrease). This error comes from reversing the subtraction order.
Why D is wrong: D: −GM/R would mean the potential decreased by GM/R when moving outward, which contradicts the fact that gravitational potential increases (toward zero) with distance.
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:
Show answer and why every option is right or wrong
Answer: D. Gravitational field is a vector — the two equal and opposite field vectors cancel at the midpoint. Gravitational potential is a scalar — both contributions are −GM/d (negative), and their algebraic sum is −2GM/d, not zero. The scalar nature of potential is the key distinction. (NCERT Class 11 Physics Chapter 7, page 135.)
Why A is wrong: A: Gravitational potential does not depend on frame of reference. It depends only on the mass configuration and the point's position relative to the masses.
Why B is wrong: B: Potential is a scalar, not a vector. It has no direction and cannot be 'anti-parallel.' This description applies to the gravitational field.
Why C is wrong: C: The kinetic energy of the test mass is irrelevant to the value of the gravitational potential at a point. Potential is a property of the field, independent of any test mass's motion.
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:
Show answer and why every option is right or wrong
Answer: D. V₁ = −GM/R (at surface, r = R). V₂ = −GM/(3R) (at r = 3R). V₁/V₂ = (−GM/R) ÷ (−GM/(3R)) = (−GM/R) × (3R/(−GM)) = 3. (NCERT Class 11 Physics Chapter 7, page 135.)
Why A is wrong: A: 1/3 is the inverse of the correct ratio. This arises from computing V₂/V₁ instead of V₁/V₂, or from confusing which point is closer to the mass.
Why B is wrong: B: 9 would apply if potential varied as 1/r² (like gravitational field strength). Potential varies as 1/r, not 1/r², so the ratio is 3, not 9. This is a common confusion between potential (1/r) and field (1/r²).
Why C is wrong: C: A ratio of 1 would mean the potential is the same at both distances, which contradicts V ∝ 1/r.
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Gravitational Potential: quick recall before you leave
How do you solve a Gravitational Potential question? A 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 135). - 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.)
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What to remember before solving Gravitational Potential questions
Which Gravitational Potential formulas do you need for NEET?
1 formula — click to collapse
Gravitational potential energy (point masses)
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
More in Gravitation: 4 exam traps and mistakes · 7 formulas · 4 question patterns from its other lessons.
Gravitational Potential questions from past NEET papers
1 question from NEET 2023. Answers verified against NTA official keys. — click to collapse
NEET 2023
1−12Gm/R
2−16Gm/R
3−20Gm/R
4−8Gm/R
NTA Answer: Option 2(final)
Sources
NCERT refs: Class 11 Physics Chapter 7, p.135
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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