How much of JEE Main comes from Gravitation?

JEEGenie estimates about 2% of JEE Main marks come from Gravitation, based on recent papers. The share varies from year to year.

Which formulas matter most in Gravitation?

The Gravitation sheet on this page has 23 formula entries, starting with Newton's Law of Gravitation, Gravitational Field, Gravitational Potential, Gravitational Potential Energy, Superposition Principle. Each one comes with when to use it and the trap to avoid.

What topics does Gravitation cover for JEE?

Gravitation covers Newton's Law of Gravitation, Gravitational Field and Potential, Kepler's Laws, Satellites and Orbital Velocity, Escape Velocity.

How should I revise Gravitation before the exam?

Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Gravitation questions on JEEGenie.

How many previous-year questions are there on Gravitation?

JEEGenie has 277 previous-year questions on Gravitation, and this page shows a few with worked explanations.

Is practice on Gravitation free on JEEGenie?

Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.

Gravitation for JEE Main & Advanced — formulas, what is asked, and traps

JEEGenie estimates about 2% of JEE Main marks come from Gravitation. This page covers 23 formula entries, each with when to use it, what JEE asks and the traps. A common slip: Forgetting that the force is always attractive and acts along the line joining the centers.

Key points to know

Newton's Law of Gravitation. Every particle attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Gravitational Field. The gravitational field at a point is the force per unit mass experienced by a test mass placed there.
Gravitational Potential. Gravitational potential at a point is the work done per unit mass in bringing a test mass from infinity to that point.
Acceleration due to Gravity (g). The acceleration experienced by an object due to Earth's gravitational pull, varying with altitude, depth, and rotation.
Gravitational Field Inside a Uniform Sphere. Inside a uniform solid sphere, the gravitational field varies linearly with distance from the center.
Gravitational Potential Inside a Uniform Sphere. Inside a uniform solid sphere, potential varies quadratically with distance.
Orbital Velocity. The velocity required for a satellite to maintain a circular orbit at a given radius.
Escape Velocity. The minimum velocity required for an object to escape Earth's gravitational pull without further propulsion.
Gravitational Potential Energy of a System of Particles. The total potential energy of a system of multiple particles is the sum of pairwise potential energies.
Gravitational Time Dilation. Time runs slower in stronger gravitational fields; a prediction of general relativity.

Formula sheet

Name	Formula	When to use
Newton's Law of Gravitation	$F = G \frac{m_{1} m_{2}}{r^{2}}$	Use to compute gravitational force between two point masses or spherically symmetric objects.
Gravitational Field	${\vec{E}}_{g} = \frac{\vec{F}}{m} = - \frac{G M}{r^{2}} \hat{r}$	Use to find the gravitational force on any mass at a point, or to find field due to a mass distribution.
Gravitational Potential	$V = - \frac{G M}{r}$	Use to compute work done by gravity or to find potential energy of a system.
Gravitational Potential Energy	$U = - \frac{G m_{1} m_{2}}{r}$	Use to compute energy of a system or to apply conservation of mechanical energy in gravitational fields.
Superposition Principle	${\vec{F}}_{n e t} = \sum {\vec{F}}_{i}$ , ${\vec{E}}_{n e t} = \sum {\vec{E}}_{i}$ , $V_{n e t} = \sum V_{i}$	Use whenever multiple masses are present, e.g., finding net force on a mass in a system.
Acceleration due to Gravity (g)	$g = \frac{G M}{R^{2}}$ (at surface)	Use to compute weight, free-fall motion, or pendulum period.
Variation of g with Altitude and Depth	$g_{h} = g (1 - \frac{2 h}{R})$ (for $h ≪ R$ ); $g_{d} = g (1 - \frac{d}{R})$ (inside Earth)	Use to compute g at a given height or depth, e.g., in satellite problems or mining.
Gravitational Field Inside a Uniform Sphere	$E_{g} = \frac{G M}{R^{3}} r$ (for $r < R$ ); $E_{g} = \frac{G M}{r^{2}}$ (for $r \geq R$ )	Use to find field inside a planet or star (assuming uniform density).
Gravitational Potential Inside a Uniform Sphere	$V = - \frac{G M}{2 R^{3}} (3 R^{2} - r^{2})$ (for $r < R$ ); $V = - \frac{G M}{r}$ (for $r \geq R$ )	Use to compute potential energy of a mass inside a planet or to find escape speed from inside.
Kepler's First Law (Law of Orbits)	Ellipse: $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ , with eccentricity $e = \sqrt{1 - \frac{b^{2}}{a^{2}}}$	Use to describe planetary motion or satellite orbits.
Kepler's Second Law (Law of Areas)	$\frac{d A}{d t} = \frac{L}{2 m} = constant$	Use to relate speed at different points in an orbit (e.g., faster at perihelion).
Kepler's Third Law (Law of Periods)	$T^{2} = \frac{4 π^{2}}{G M} a^{3}$	Use to find period of a satellite or planet, or to compare orbits.
Orbital Velocity	$v_{o} = \sqrt{\frac{G M}{r}}$	Use to find speed of a satellite in circular orbit.
Escape Velocity	$v_{e} = \sqrt{\frac{2 G M}{R}} = \sqrt{2 g R}$	Use to determine if an object can leave a planet's gravity.
Energy of an Orbiting Satellite	$E = - \frac{G M m}{2 r}$ (kinetic: $\frac{G M m}{2 r}$ , potential: $- \frac{G M m}{r}$ )	Use to compute energy required to change orbit or to find binding energy.
Geostationary and Polar Satellites	Geostationary: $T = 24 h$ , $r \approx 42, 000 km$ from Earth's center	Use to describe communication satellites (geostationary) or remote sensing (polar).
Weightlessness	Apparent weight = $m (g - a)$ ; in free fall $a = g$ , so weight = 0	Use to explain phenomena in spacecraft or elevators.
Gravitational Binding Energy	$U_{b i n d} = \frac{3 G M^{2}}{5 R}$ (for uniform sphere)	Use to compute energy released in formation of a star or planet.
Gravitational Potential Energy of a System of Particles	$U_{t o t a l} = - \sum_{i < j} \frac{G m_{i} m_{j}}{r_{i j}}$	Use to find total energy of a system of point masses (e.g., stars in a cluster).
Gravitational Lensing	Deflection angle $θ = \frac{4 G M}{c^{2} b}$ (where $b$ is impact parameter)	Use to explain astronomical observations like Einstein rings.
Gravitational Time Dilation	$Δ t^{'} = Δ t \sqrt{1 - \frac{2 G M}{r c^{2}}}$	Use to explain GPS corrections or time differences near massive objects.
Black Holes and Schwarzschild Radius	$R_{s} = \frac{2 G M}{c^{2}}$	Use to determine if an object will become a black hole (if $R < R_{s}$ ).
Tidal Forces	Tidal acceleration difference $Δ a \approx \frac{2 G M}{r^{3}} Δ r$	Use to explain ocean tides, Roche limit, or spaghettification near black holes.

Open the Gravitation formula page

What JEE asks

Newton's Law of Gravitation. JEE often asks for force between two objects with given masses and distance, or comparing forces in different configurations.
Gravitational Field. JEE may ask to find field due to a ring, disc, or spherical shell using integration or superposition.
Gravitational Potential. JEE often asks to find potential due to multiple masses or to relate potential and field ( $E = - d V / d r$ ).
Gravitational Potential Energy. JEE may ask to find escape speed or orbital energy using potential energy.
Superposition Principle. JEE often tests with symmetric arrangements (e.g., masses at vertices of a square) to exploit cancellation.
Acceleration due to Gravity (g). JEE often asks for variation of $g$ with height/depth, or effective $g$ due to rotation.
Variation of g with Altitude and Depth. JEE may ask to compare g at different points or find depth where g is half.
Gravitational Field Inside a Uniform Sphere. JEE may ask to plot field vs. distance or find force on a mass inside Earth.
Gravitational Potential Inside a Uniform Sphere. JEE may ask to find work done to move a mass from center to surface.
Kepler's First Law (Law of Orbits). JEE may ask about aphelion/perihelion distances or eccentricity.
Kepler's Second Law (Law of Areas). JEE may ask to find ratio of speeds at aphelion and perihelion.
Kepler's Third Law (Law of Periods). JEE often asks to find period of a satellite given altitude or to compare periods of two planets.
Orbital Velocity. JEE may ask to find orbital speed for a given height or to compare speeds of different satellites.
Escape Velocity. JEE often asks to compute escape speed from Earth or other planets, or to compare with orbital speed.
Energy of an Orbiting Satellite. JEE may ask to find work needed to move satellite to a higher orbit or to escape.
Geostationary and Polar Satellites. JEE may ask to find height of geostationary satellite or compare periods.
Weightlessness. JEE may ask about apparent weight in accelerating frames or in orbit.
Gravitational Binding Energy. JEE may ask to compare binding energies of different celestial bodies.
Gravitational Potential Energy of a System of Particles. JEE may ask to find work done to assemble a system from infinity.
Gravitational Lensing. JEE may ask conceptual questions about light bending near massive bodies.
Gravitational Time Dilation. JEE may ask conceptual questions about time dilation near Earth vs. space.
Black Holes and Schwarzschild Radius. JEE may ask to compute Schwarzschild radius for a given mass or compare with Earth's radius.
Tidal Forces. JEE may ask to compare tidal forces from different bodies or find Roche limit.

Common traps

Forgetting that the force is always attractive and acts along the line joining the centers. Newton's Law of Gravitation
Confusing field with force; field is a property of space, force depends on test mass. Gravitational Field
Forgetting that potential is always negative (zero at infinity). Gravitational Potential
Forgetting the negative sign; it indicates bound system. Gravitational Potential Energy
Forgetting that force and field are vectors; adding them without considering direction. Superposition Principle
Confusing $g$ with $G$ ; $g$ varies, $G$ is constant. Acceleration due to Gravity (g)
Using the altitude formula for large $h$ ; use $g_{h} = \frac{G M}{(R + h)^{2}}$ instead. Variation of g with Altitude and Depth
Forgetting that field inside a spherical shell is zero. Gravitational Field Inside a Uniform Sphere
Forgetting that potential is continuous at $r = R$ . Gravitational Potential Inside a Uniform Sphere
Thinking orbits are circular; they are elliptical (circular is a special case). Kepler's First Law (Law of Orbits)
Forgetting that this law implies angular momentum is conserved. Kepler's Second Law (Law of Areas)
Forgetting that $M$ is the mass of the central body. Kepler's Third Law (Law of Periods)
Forgetting that $r$ is distance from center, not altitude above surface. Orbital Velocity
Forgetting that escape velocity is independent of mass of the object. Escape Velocity

Topics in Gravitation

Newton's Law of Gravitation
Gravitational Field and Potential
Kepler's Laws
Satellites and Orbital Velocity
Escape Velocity

Previous-year questions on Gravitation

JEEGenie has 277 previous-year questions on Gravitation. A few worked examples follow.

Year	Questions
2026	10
2025	15
2024	26
2023	40
2022	27
2021	35
2020	16
2019	27
2018	5
2017	6
2016	4
2015	8
2014	3
2013	5
2012	6
2011	1
2010	2
2009	1
2008	4
2007	1
2006	1
2005	3
2004	4
2003	3
2002	6
2001	1
1998	1
1997	1
1996	1
1994	1
1993	1
1990	1
1988	3
1987	1
1986	2
1985	1
1984	3
1981	1

Question 1 easy

A planet (

P_{1}

) is moving around the star of mass

2 M

in the orbit of radius

R

. Another planet (

P_{2}

) is moving around another star of mass

4 M

in a orbit of radius

2 R

. Ratio of time periods of revolution of

P_{2}

and

P_{1}

is ________.

$\frac{1}{2}$
$2$
$4$
$\frac{1}{4}$

Answer: B

Explanation. For a planet orbiting a star of mass

M

in a circular orbit of radius

R

, Kepler's third law gives

T^{2} = \frac{4 π^{2}}{G M} R^{3} .

For

P_{1}

: star mass

2 M

, radius

R

T_{1}^{2} = \frac{4 π^{2}}{G (2 M)} R^{3} = \frac{2 π^{2} R^{3}}{G M} .

For

P_{2}

: star mass

4 M

, radius

2 R

T_{2}^{2} = \frac{4 π^{2}}{G (4 M)} (2 R)^{3} = \frac{4 π^{2}}{4 G M} \cdot 8 R^{3} = \frac{8 π^{2} R^{3}}{G M} .

Divide the two:

\frac{T_{2}^{2}}{T_{1}^{2}} = \frac{\frac{8 π^{2} R^{3}}{G M}}{\frac{2 π^{2} R^{3}}{G M}} = 4.

Taking square root:

\frac{T_{2}}{T_{1}} = 2.

B

From NTA/IIT papers: JEE Main 2026 · 2 Apr Shift 1

Question 2 medium

Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length

a

. When released, they interact only through gravitational force and collide after a time

T = 4

seconds. If the sides of the triangle are increased to length

2 a

and also the masses of the spheres are made 2 m , then they will collide after__________seconds.

Answer: 8

Explanation. Let each sphere have mass

m

and side length

a

. The acceleration due to gravitational attraction scales as

a \propto \frac{G m}{a^{2}}

. The time to collide scales as

T \propto \sqrt{\frac{a^{3}}{G m}}

. If side becomes

2 a

and mass becomes

2 m

, then new time

T^{'} \propto \sqrt{\frac{(2 a)^{3}}{G (2 m)}} = \sqrt{\frac{8 a^{3}}{2 G m}} = \sqrt{4 \cdot \frac{a^{3}}{G m}} = 2 T

. Given

T = 4

s, so

T^{'} = 2 \times 4 = 8

8

From NTA/IIT papers: JEE Main 2025 · 3 Apr Shift 1

Question 3 hard

A particle of mass

m

is under the influence of the gravitational field of a body of mass

M (≫ m)

. The particle is moving in a circular orbit of radius

r_{0}

with time period

T_{0}

around the mass

M

. Then, the particle is subjected to an additional central force, corresponding to the potential energy

V_{c} (r) = m α / r^{3}

, where

α

is a positive constant of suitable dimensions and

r

is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius

r_{0}

in the combined gravitational potential due to

M

and

V_{c} (r)

, but with a new time period

T_{1}

, then

(T_{1}^{2} - T_{0}^{2}) / T_{1}^{2}

is given by [

G

is the gravitational constant.]

$\frac{3 α}{G M r_{0}^{2}}$
$\frac{α}{2 G M r_{0}^{2}}$
$\frac{α}{G M r_{0}^{2}}$
$\frac{2 α}{G M r_{0}^{2}}$

Answer: A

Explanation. For a circular orbit, the centripetal force equals the radial force from the potential. The gravitational potential is

V_{g} (r) = - \frac{G M m}{r} .

The additional potential is

V_{c} (r) = \frac{m α}{r^{3}} .

Thus the total potential is

V (r) = - \frac{G M m}{r} + \frac{m α}{r^{3}} .

The radial force is

F_{r} = - \frac{d V}{d r} = - \frac{G M m}{r^{2}} + \frac{3 m α}{r^{4}} .

For circular motion at radius

r_{0}

m ω^{2} r_{0} = \frac{G M m}{r_{0}^{2}} - \frac{3 m α}{r_{0}^{4}} .

Divide by

m

ω^{2} r_{0} = \frac{G M}{r_{0}^{2}} - \frac{3 α}{r_{0}^{4}} .

ω^{2} = \frac{G M}{r_{0}^{3}} - \frac{3 α}{r_{0}^{5}} .

The original angular frequency (without the extra force) is

ω_{0}^{2} = \frac{G M}{r_{0}^{3}} .

Since

T = 2 π / ω

\frac{T_{1}^{2}}{T_{0}^{2}} = \frac{ω_{0}^{2}}{ω_{1}^{2}} = \frac{G M / r_{0}^{3}}{G M / r_{0}^{3} - 3 α / r_{0}^{5}} .

Thus

\frac{T_{1}^{2} - T_{0}^{2}}{T_{1}^{2}} = 1 - \frac{T_{0}^{2}}{T_{1}^{2}} = 1 - \frac{ω_{1}^{2}}{ω_{0}^{2}} = \frac{3 α / r_{0}^{5}}{G M / r_{0}^{3}} = \frac{3 α}{G M r_{0}^{2}} .

A) \frac{3 α}{G M r_{0}^{2}}

From NTA/IIT papers: JEE Advanced 2024

Question 4 medium

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing

W

on earth will weigh on that planet:

$2^{2 / 3} W$
W
$2 W$
$2^{1 / 3} W$

Answer: D

Explanation. Given: -

M_{p} = 2 M_{e}

ρ_{p} = ρ_{e}

Since density

ρ = \frac{M}{\frac{4}{3} π R^{3}}

, we have:

\frac{M_{p}}{R_{p}^{3}} = \frac{M_{e}}{R_{e}^{3}}

\frac{2 M_{e}}{R_{p}^{3}} = \frac{M_{e}}{R_{e}^{3}} ⟹ R_{p}^{3} = 2 R_{e}^{3} ⟹ R_{p} = 2^{1 / 3} R_{e}

Weight on a planet is

W = m g = \frac{G M m}{R^{2}}

. So weight on the planet:

W_{p} = \frac{G M_{p} m}{R_{p}^{2}} = \frac{G (2 M_{e}) m}{(2^{1 / 3} R_{e})^{2}}

= \frac{2 G M_{e} m}{2^{2 / 3} R_{e}^{2}} = 2^{1 / 3} \frac{G M_{e} m}{R_{e}^{2}} = 2^{1 / 3} W

Therefore, the object weighs

2^{1 / 3} W

on that planet.

D

From NTA/IIT papers: JEE Main 2023 · 6 Apr Shift 1

Question 5 hard

Two spherical stars

A

and

B

have densities

ρ_{A}

and

ρ_{B}

, respectively.

A

and

B

have the same radius, and their masses

M_{A}

and

M_{B}

are related by

M_{B} = 2 M_{A}

. Due to an interaction process, star

A

loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains

ρ_{A}

. The entire mass lost by

A

is deposited as a thick spherical shell on

B

with the density of the shell being

ρ_{A}

. If

v_{A}

and

v_{B}

are the escape velocities from

A

and

B

after the interaction process, the ratio

\frac{v_{B}}{v_{A}} = \sqrt{\frac{10 n}{15^{1 / 3}}}

. The value of

n

is ______.

Answer: 2.30

Explanation. We have initial masses

M_{B} = 2 M_{A}

, same radius

R

, so

ρ_{B} = \frac{M_{B}}{\frac{4}{3} π R^{3}} = 2 ρ_{A} .

After interaction: **For star A:** Mass lost: let final mass be

M_{A}^{'}

. Radius becomes

R / 2

, density remains

ρ_{A}

M_{A}^{'} = ρ_{A} \cdot \frac{4}{3} π {(\frac{R}{2})}^{3} = \frac{1}{8} ρ_{A} \cdot \frac{4}{3} π R^{3} = \frac{M_{A}}{8} .

So mass lost by A:

Δ M = M_{A} - \frac{M_{A}}{8} = \frac{7}{8} M_{A} .

**For star B:** This

\frac{7}{8} M_{A}

is added as a shell of density

ρ_{A}

. Original

B

has mass

2 M_{A}

and radius

R

. The shell has volume

V_{shell} = \frac{Δ M}{ρ_{A}} = \frac{7}{8} \frac{M_{A}}{ρ_{A}} = \frac{7}{8} \cdot \frac{4}{3} π R^{3} = \frac{7}{6} π R^{3} .

If shell outer radius is

R_{B}

, inner radius is

R

(original B radius),

\frac{4}{3} π (R_{B}^{3} - R^{3}) = \frac{7}{6} π R^{3}

R_{B}^{3} - R^{3} = \frac{7}{8} R^{3} \Rightarrow R_{B}^{3} = \frac{15}{8} R^{3}

R_{B} = R {(\frac{15}{8})}^{1 / 3} .

Final mass of B:

M_{B}^{'} = 2 M_{A} + \frac{7}{8} M_{A} = \frac{23}{8} M_{A} .

**Escape velocities:** For A:

v_{A} = \sqrt{\frac{2 G M_{A}^{'}}{R / 2}} = \sqrt{\frac{2 G (M_{A} / 8)}{R / 2}} = \sqrt{\frac{G M_{A}}{2 R}} .

For B:

v_{B} = \sqrt{\frac{2 G M_{B}^{'}}{R_{B}}} = \sqrt{\frac{2 G \cdot \frac{23}{8} M_{A}}{R (15 / 8)^{1 / 3}}} .

Ratio:

\frac{v_{B}}{v_{A}} = \sqrt{\frac{\frac{23}{4} \frac{G M_{A}}{R}}{\frac{G M_{A}}{2 R} \cdot (15 / 8)^{1 / 3}}} = \sqrt{\frac{23}{4} \cdot \frac{2}{(15 / 8)^{1 / 3}}} = \sqrt{\frac{23}{2} \cdot \frac{8^{1 / 3}}{15^{1 / 3}}} .

Since

8^{1 / 3} = 2

\frac{v_{B}}{v_{A}} = \sqrt{\frac{23}{2} \cdot \frac{2}{15^{1 / 3}}} = \sqrt{\frac{23}{15^{1 / 3}}} .

Given

\frac{v_{B}}{v_{A}} = \sqrt{\frac{10 n}{15^{1 / 3}}},

we equate:

23 = 10 n \Rightarrow n = 2.3.

2.30

From NTA/IIT papers: JEE Advanced 2022

Frequently asked questions

How much of JEE Main comes from Gravitation?: JEEGenie estimates about 2% of JEE Main marks come from Gravitation, based on recent papers. The share varies from year to year.
Which formulas matter most in Gravitation?: The Gravitation sheet on this page has 23 formula entries, starting with Newton's Law of Gravitation, Gravitational Field, Gravitational Potential, Gravitational Potential Energy, Superposition Principle. Each one comes with when to use it and the trap to avoid.
What topics does Gravitation cover for JEE?: Gravitation covers Newton's Law of Gravitation, Gravitational Field and Potential, Kepler's Laws, Satellites and Orbital Velocity, Escape Velocity.
How should I revise Gravitation before the exam?: Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Gravitation questions on JEEGenie.
How many previous-year questions are there on Gravitation?: JEEGenie has 277 previous-year questions on Gravitation, and this page shows a few with worked explanations.
Is practice on Gravitation free on JEEGenie?: Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.