IIT JEE Test Series — Practice smarter, perform stronger.

Gravitation formulas

Master Gravitation through 32 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

Practise these formulas Know more about IIT JEE

Back to Formula Book

Gravitation, every formula

32 formulas, typeset and free. Print it, or keep it open beside your practice.

Universal law of gravitation
$F = \frac{G m _{1} m _{2}}{r ^{2}}$
Q1MCQUniversal law
The gravitational force between two masses varies as:
- A
  $\dfrac{1}{r^{2}}$
- B
  $r^{2}$
- C
  $\dfrac{1}{r}$
- D
  $r$
Gravitational constant
$G = 6.67 \times 1 0^{- 11} N m^{2} kg^{- 2}$
Q1MCQG
The SI unit of $G$ is:
- A
  N m$^2$ kg$^{-2}$
- B
  N kg$^{-1}$
- C
  m/s$^2$
- D
  N
Gravitational field
$E = \frac{F}{m} = \frac{GM}{r ^{2}}$
Q1MCQField
The gravitational field of a point mass $M$ is:
- A
  $\dfrac{GM}{r^{2}}$
- B
  $\dfrac{GM}{r}$
- C
  $GMr$
- D
  $\dfrac{GM}{r^{3}}$
Acceleration due to gravity
$g = \frac{GM}{R ^{2}}$
Q1MCQg
The acceleration due to gravity at the surface is:
- A
  $\dfrac{GM}{R^{2}}$
- B
  $\dfrac{GM}{R}$
- C
  $\dfrac{GM}{R^{3}}$
- D
  $GMR$
Variation with height (h≪R)
$g_{h} \approx g (1 - \frac{2 h}{R})$
Q1MCQHeight variation
At height $h\ll R$, $g$ becomes approximately:
- A
  $g\left(1-\dfrac{2h}{R}\right)$
- B
  $g\left(1+\dfrac{2h}{R}\right)$
- C
  $g\left(1-\dfrac{h}{R}\right)$
- D
  $g$
Variation with height (exact)
$g_{h} = \frac{GM}{( R + h ) ^{2}}$
Q1MCQExact height
At height $h$, the exact value of $g$ is:
- A
  $\dfrac{GM}{(R+h)^{2}}$
- B
  $\dfrac{GM}{R^{2}}$
- C
  $\dfrac{GM}{R+h}$
- D
  $g$
Variation with depth
$g_{d} = g (1 - \frac{d}{R})$
Q1MCQDepth variation
At depth $d$, $g$ becomes:
- A
  $g\left(1-\dfrac{d}{R}\right)$
- B
  $g\left(1-\dfrac{2d}{R}\right)$
- C
  $g\left(1+\dfrac{d}{R}\right)$
- D
  $g$
Effect of rotation
$g^{'} = g - R ω^{2} cos^{2} λ$
λ = latitude
Q1MCQRotation
Earth's rotation makes $g$ vary with latitude $\lambda$ as:
- A
  $g-R\omega^{2}\cos^{2}\lambda$
- B
  $g+R\omega^{2}\cos^{2}\lambda$
- C
  $g\cos\lambda$
- D
  $g$
Gravitational potential
$V = - \frac{GM}{r}$
Q1MCQPotential
The gravitational potential of a point mass is:
- A
  $-\dfrac{GM}{r}$
- B
  $-\dfrac{GM}{r^{2}}$
- C
  $\dfrac{GM}{r}$
- D
  $\dfrac{GM}{r^{2}}$
Field from potential
$E = - \frac{d V}{d r}$
Q1MCQField from potential
The gravitational field relates to potential by:
- A
  $E=-\dfrac{dV}{dr}$
- B
  $E=\dfrac{dV}{dr}$
- C
  $E=V r$
- D
  $E=-V$
Gravitational PE
$U = - \frac{GM m}{r}$
Q1MCQPE
The gravitational PE of two masses is:
- A
  $-\dfrac{GMm}{r}$
- B
  $-\dfrac{GMm}{r^{2}}$
- C
  $\dfrac{GMm}{r}$
- D
  $mgh$ always
Escape velocity
$v_{e} = \frac{2 GM}{R} = 2 g R \approx 11.2 km/s$
Q1MCQEscape velocity
The escape velocity from Earth's surface is about:
- A
  $11.2$ km/s
- B
  $7.9$ km/s
- C
  $5.6$ km/s
- D
  $22.4$ km/s
Orbital velocity
$v_{o} = \frac{GM}{r}$
Q1MCQOrbital velocity
The orbital velocity of a satellite is:
- A
  $\sqrt{\dfrac{GM}{r}}$
- B
  $\sqrt{\dfrac{2GM}{r}}$
- C
  $\dfrac{GM}{r}$
- D
  $\sqrt{GMr}$
Orbital velocity near surface
$v_{o} = g R \approx 7.9 km/s$
Q1MCQNear-surface orbital
The orbital speed just above Earth's surface is about:
- A
  $7.9$ km/s
- B
  $11.2$ km/s
- C
  $5.6$ km/s
- D
  $3.9$ km/s
Escape–orbital relation
$v_{e} = 2 v_{o}$
Q1MCQEscape–orbital
The escape velocity is related to orbital velocity by:
- A
  $v_e=\sqrt2\,v_o$
- B
  $v_e=v_o$
- C
  $v_e=2v_o$
- D
  $v_e=\dfrac{v_o}{\sqrt2}$
Time period of a satellite
$T = 2 π \frac{r ^{3}}{GM}$
Q1MCQSatellite period
The period of a satellite is:
- A
  $2\pi\sqrt{\dfrac{r^{3}}{GM}}$
- B
  $2\pi\sqrt{\dfrac{r}{GM}}$
- C
  $2\pi\sqrt{\dfrac{GM}{r^{3}}}$
- D
  $2\pi\dfrac{r^{3}}{GM}$
Minimum time period
$T = 2 π \frac{R}{g} \approx 84.6 min$
Q1MCQMin period
The minimum period of an Earth satellite is about:
- A
  $84.6$ min
- B
  $24$ h
- C
  $90$ h
- D
  $12$ h
KE of a satellite
$K = \frac{GM m}{2 r}$
Q1MCQSatellite KE
The kinetic energy of a satellite is:
- A
  $\dfrac{GMm}{2r}$
- B
  $-\dfrac{GMm}{r}$
- C
  $-\dfrac{GMm}{2r}$
- D
  $\dfrac{GMm}{r}$
PE of a satellite
$U = - \frac{GM m}{r}$
Q1MCQSatellite PE
The potential energy of a satellite is:
- A
  $-\dfrac{GMm}{r}$
- B
  $\dfrac{GMm}{2r}$
- C
  $-\dfrac{GMm}{2r}$
- D
  $\dfrac{GMm}{r}$
Total energy of a satellite
$E = - \frac{GM m}{2 r}$
Q1MCQSatellite total energy
The total energy of a satellite is:
- A
  $-\dfrac{GMm}{2r}$
- B
  $\dfrac{GMm}{2r}$
- C
  $-\dfrac{GMm}{r}$
- D
  $0$
Kepler's first law
$orbit is an ellipse with the Sun at a focus$
Q1MCQKepler 1st law
Kepler's first law states that a planet's orbit is:
- A
  an ellipse with the Sun at a focus
- B
  a circle centred on the Sun
- C
  a parabola
- D
  a straight line
Kepler's second law (areal velocity)
$\frac{d A}{d t} = \frac{L}{2 m} = constant$
Q1MCQKepler 2nd law
Kepler's second law implies that the areal velocity is:
- A
  constant
- B
  increasing
- C
  zero
- D
  proportional to $r$
Kepler's third law
$T^{2} \propto r^{3}$
Q1MCQKepler 3rd law
Kepler's third law states:
- A
  $T^{2}\propto r^{3}$
- B
  $T\propto r$
- C
  $T^{3}\propto r^{2}$
- D
  $T^{2}\propto r$
Field of a ring (on axis)
$E = \frac{GM r}{( a ^{2} + r ^{2} ) ^{3/2}}$
Q1MCQRing field
The gravitational field on the axis of a ring is:
- A
  $\dfrac{GMr}{(a^{2}+r^{2})^{3/2}}$
- B
  $\dfrac{GM}{r^{2}}$
- C
  $\dfrac{GM}{a^{2}}$
- D
  $0$
Field inside a solid sphere
$E = \frac{GM r}{a ^{3}}$
r<a
Q1MCQInside solid sphere
The field at distance $r<a$ inside a uniform solid sphere is:
- A
  $\dfrac{GMr}{a^{3}}$
- B
  $\dfrac{GM}{r^{2}}$
- C
  $0$
- D
  $\dfrac{GM}{a^{2}}$
Potential at centre of a solid sphere
$V = - \frac{3 GM}{2 a}$
Q1MCQCentre potential
The potential at the centre of a uniform solid sphere is:
- A
  $-\dfrac{3GM}{2a}$
- B
  $-\dfrac{GM}{a}$
- C
  $0$
- D
  $-\dfrac{GM}{2a}$
Field inside a shell
$E = 0$
r<a
Potential inside a shell
$V = - \frac{GM}{a}$
r<a
Q1MCQPotential inside shell
The potential inside a spherical shell of radius $a$ is:
- A
  $-\dfrac{GM}{a}$
- B
  $0$
- C
  $-\dfrac{GM}{r}$
- D
  $-\dfrac{3GM}{2a}$
g at pole vs equator
$g_{p o l e} > g_{e q u a t or}$
Q1MCQPole vs equator
The value of $g$ is:
- A
  greater at the poles
- B
  greater at the equator
- C
  equal everywhere
- D
  zero at the poles
Tunnel oscillation period
$T = 2 π \frac{R}{g}$
Q1MCQTunnel oscillation
The period of oscillation through a tunnel across Earth is:
- A
  $2\pi\sqrt{\dfrac{R}{g}}$
- B
  $2\pi\sqrt{\dfrac{g}{R}}$
- C
  $2\pi\sqrt{\dfrac{R^{3}}{GM}}$
- D
  $2\pi\sqrt{R}$
Maximum height (projectile)
$H = \frac{v ^{2}}{2 g - \frac{v ^{2}}{R}}$
Q1MCQMax height
The maximum height of a body projected up with speed $v$ (not small) is:
- A
  $\dfrac{v^{2}}{2g-\tfrac{v^{2}}{R}}$
- B
  $\dfrac{v^{2}}{2g}$
- C
  $\dfrac{v^{2}}{g}$
- D
  $vR$
Geostationary broadcast angle
$θ = cos^{- 1} (\frac{R}{R + h})$
Q1MCQBroadcast angle
The half-angle of a geostationary satellite's broadcast region is:
- A
  $\cos^{-1}\!\left(\dfrac{R}{R+h}\right)$
- B
  $\sin^{-1}\!\left(\dfrac{R}{R+h}\right)$
- C
  $\tan^{-1}\!\left(\dfrac{R}{h}\right)$
- D
  $\dfrac{R}{R+h}$

Other ways to revise this chapter

Master this chapter with similar other learning materials.

Preparing students for India’s top institutes

Our students are currently into top technological and medical institutes of India.

IIT Bombay
IIT Delhi
IIT Madras
IIT Kanpur
IIT Kharagpur
IIT Roorkee
IIT Guwahati
IIT BHU Varanasi
AIIMS Delhi
NIT Tiruchirappalli
NIT Rourkela
IIT Bombay
IIT Delhi
IIT Madras
IIT Kanpur
IIT Kharagpur
IIT Roorkee
IIT Guwahati
IIT BHU Varanasi
AIIMS Delhi
NIT Tiruchirappalli
NIT Rourkela

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Gravitation formulas

Gravitation, every formula

Universal law of gravitation

Gravitational constant

Gravitational field

Acceleration due to gravity

Variation with height (h≪R)

Variation with height (exact)

Variation with depth

Effect of rotation

Gravitational potential

Field from potential

Gravitational PE

Escape velocity

Orbital velocity

Orbital velocity near surface

Escape–orbital relation

Time period of a satellite

Minimum time period

KE of a satellite

PE of a satellite

Total energy of a satellite

Kepler's first law

Kepler's second law (areal velocity)

Kepler's third law

Field of a ring (on axis)

Field inside a solid sphere

Potential at centre of a solid sphere

Field inside a shell

Potential inside a shell

g at pole vs equator

Tunnel oscillation period

Maximum height (projectile)

Geostationary broadcast angle

More JEE Advanced Physics formula sheets

Other ways to revise this chapter

Preparing students for India’s top institutes

Join QuestPix, Today!