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Gravitational Field and Energy

Master gravitational field, field intensity, point mass fields, field due to sphere, field graphs, binding energy, numericals and PYQs with clean NCERT-style diagrams.

CBSENEETJEE MainJEE AdvancedIBIGCSEA-Level

Gravitational Field

A gravitational field is the region around a mass in which another mass experiences gravitational force. It is invisible, but its direction and strength can be represented using field lines.

Core Idea

Mass creates gravitational field. A test mass placed in that field experiences an attractive force.

Direction

Field direction is the direction of force on a small positive test mass, so it is toward the attracting mass.

Field Lines

Field Intensity

Gravitational field intensity at a point is gravitational force experienced by unit mass placed at that point.

g = F/m

Unit: N kg^-1

Also: m s^-2

Meaning

If a mass m experiences force F, the gravitational field intensity is F divided by m. Near Earth's surface, it is approximately 9.8 N kg^-1.

Direction Diagram

Field Due to Point Mass

For an isolated point mass M, gravitational field intensity at distance r is found by dividing Newton's gravitational force by test mass.

F = GMm/r²

g = F/m = GM/r²

Vector direction: toward M

Point Mass Field

Exam Notes

Magnitude decreases as 1/r².
Direction is radially inward.
Field is independent of test mass.
Lines are closer where field is stronger.

Field Due to Sphere and Shell

For points outside a uniform sphere, the sphere behaves as if its whole mass is concentrated at its centre. Inside a uniform solid sphere, field increases linearly with distance from centre. Inside a thin shell, field is zero.

Outside Sphere

g = GM/r²

Inside Solid Sphere

g = GMr/R³

Inside Shell

g = 0

Field Graphs

Graphs make the sphere concepts exam-friendly. For a solid sphere, g rises linearly from centre to surface, then decreases as inverse square outside. For a shell, g is zero inside and jumps at the shell surface, then follows inverse square outside.

Uniform Solid Sphere

Shell Concept Graph

Binding Energy Concept

Binding energy is the energy required to remove a body from a bound gravitational state to infinity. For a circular satellite, total energy is negative and binding energy is the positive magnitude of that total energy.

U = -GMm/r

K = GMm/2r

E = -GMm/2r

Binding Energy = GMm/2r

Smooth Satellite Motion

Energy Meaning

Negative total energy means bound orbit.
Zero total energy means just escaped.
Positive total energy means unbound path.
More negative energy means stronger binding.

Formula and Concept Table

Concept	Formula	Meaning	Exam Tip
Field intensity	g = F/m	Force per unit mass.	Vector direction matters.
Point mass field	g = GM/r²	Field at distance r.	Valid outside spherical body too.
Solid sphere inside	g = GMr/R³	Linear variation inside.	g = 0 at centre.
Thin shell inside	g = 0	Net pull cancels.	Very common conceptual question.
Potential energy	U = -GMm/r	Energy of mass pair.	Zero at infinity.
Binding energy in orbit	GMm/2r	Energy needed to escape from circular orbit.	Do not confuse with GMm/r from surface.

High-Quality Numericals

Solutions are hidden by default for interactive practice. Click Show Solution to reveal complete steps.

Field Intensity

Question: Find gravitational field intensity at distance r from point mass M.

Show Solution

Given: Mass = M, distance = r

Formula: g = GM/r²

Calculation: Direct substitution gives g = GM/r² toward M.

Final Answer: GM/r², toward the mass

Exam Tip: Direction is always toward attracting mass.

Common Mistake: Do not write direction away from mass.

Point Mass Ratio

Question: If distance from a mass is doubled, how does field intensity change?

Show Solution

Given: r2 = 2r1

Formula: g proportional to 1/r²

Calculation: g2/g1 = (r1/r2)² = 1/4

Final Answer: Field becomes one-fourth.

Exam Tip: Inverse-square relation is a favorite MCQ.

Common Mistake: Do not use inverse relation only.

Sphere Surface

Question: A planet has mass M and radius R. Write field at surface.

Show Solution

Given: M, R

Formula: g = GM/R²

Calculation: At surface use r=R.

Final Answer: GM/R²

Exam Tip: For outside points sphere behaves like point mass at centre.

Common Mistake: Do not use diameter.

Inside Solid Sphere

Question: For uniform solid sphere, find how g varies inside.

Show Solution

Given: r < R

Formula: g = GMr/R³

Calculation: Inside enclosed mass is proportional to r³, so g proportional to r.

Final Answer: g = GMr/R³

Exam Tip: Graph is straight line from centre to surface.

Common Mistake: Do not use GM/r² inside solid sphere.

Shell Interior

Question: What is gravitational field inside a thin spherical shell?

Show Solution

Given: Inside shell

Formula: Shell theorem

Calculation: Net field inside a uniform shell is zero.

Final Answer: g = 0

Exam Tip: Good conceptual PYQ point.

Common Mistake: Do not confuse shell with solid sphere.

Binding Energy

Question: Write binding energy of a satellite of mass m in circular orbit radius r around mass M.

Show Solution

Given: M, m, r

Formula: E = -GMm/2r, BE = -E

Calculation: BE = GMm/2r

Final Answer: GMm/2r

Exam Tip: Binding energy is positive amount required to remove satellite.

Common Mistake: Do not write total energy as binding energy sign.

Escape From Surface

Question: Energy required to remove mass m from planet surface to infinity.

Show Solution

Given: Planet M, radius R

Formula: U = -GMm/R

Calculation: Required energy = 0 - (-GMm/R)

Final Answer: GMm/R

Exam Tip: This is gravitational binding from surface.

Common Mistake: Do not include 1/2 unless circular orbit is mentioned.

Graph Maximum

Question: Where is field maximum for uniform solid sphere?

Show Solution

Given: Solid sphere radius R

Formula: Inside g proportional r; outside g proportional 1/r2

Calculation: g increases up to surface then decreases.

Final Answer: At r = R

Exam Tip: Surface is graph peak.

Common Mistake: Do not say centre.

Field Direction

Question: A small test mass is placed near Earth. What is direction of field intensity?

Show Solution

Given: Near Earth

Formula: Field is force per unit mass

Calculation: Attractive force is toward Earth's centre.

Final Answer: Toward Earth's centre

Exam Tip: Field direction is direction of force on test mass.

Common Mistake: Do not say along velocity.

Mass From Field

Question: At distance r, field is g. Find central mass M.

Show Solution

Given: g, r

Formula: g = GM/r2

Calculation: M = gr²/G

Final Answer: gr²/G

Exam Tip: Useful for planetary mass problems.

Common Mistake: Do not forget square on r.

Field Intensity

Question: Find gravitational field intensity at distance r from point mass M.

Show Solution

Given: Mass = M, distance = r

Formula: g = GM/r²

Calculation: Direct substitution gives g = GM/r² toward M.

Final Answer: GM/r², toward the mass

Exam Tip: Direction is always toward attracting mass.

Common Mistake: Do not write direction away from mass.

Point Mass Ratio

Question: If distance from a mass is doubled, how does field intensity change?

Show Solution

Given: r2 = 2r1

Formula: g proportional to 1/r²

Calculation: g2/g1 = (r1/r2)² = 1/4

Final Answer: Field becomes one-fourth.

Exam Tip: Inverse-square relation is a favorite MCQ.

Common Mistake: Do not use inverse relation only.

Sphere Surface

Question: A planet has mass M and radius R. Write field at surface.

Show Solution

Given: M, R

Formula: g = GM/R²

Calculation: At surface use r=R.

Final Answer: GM/R²

Exam Tip: For outside points sphere behaves like point mass at centre.

Common Mistake: Do not use diameter.

Inside Solid Sphere

Question: For uniform solid sphere, find how g varies inside.

Show Solution

Given: r < R

Formula: g = GMr/R³

Calculation: Inside enclosed mass is proportional to r³, so g proportional to r.

Final Answer: g = GMr/R³

Exam Tip: Graph is straight line from centre to surface.

Common Mistake: Do not use GM/r² inside solid sphere.

Shell Interior

Question: What is gravitational field inside a thin spherical shell?

Show Solution

Given: Inside shell

Formula: Shell theorem

Calculation: Net field inside a uniform shell is zero.

Final Answer: g = 0

Exam Tip: Good conceptual PYQ point.

Common Mistake: Do not confuse shell with solid sphere.

Binding Energy

Question: Write binding energy of a satellite of mass m in circular orbit radius r around mass M.

Show Solution

Given: M, m, r

Formula: E = -GMm/2r, BE = -E

Calculation: BE = GMm/2r

Final Answer: GMm/2r

Exam Tip: Binding energy is positive amount required to remove satellite.

Common Mistake: Do not write total energy as binding energy sign.

Escape From Surface

Question: Energy required to remove mass m from planet surface to infinity.

Show Solution

Given: Planet M, radius R

Formula: U = -GMm/R

Calculation: Required energy = 0 - (-GMm/R)

Final Answer: GMm/R

Exam Tip: This is gravitational binding from surface.

Common Mistake: Do not include 1/2 unless circular orbit is mentioned.

Graph Maximum

Question: Where is field maximum for uniform solid sphere?

Show Solution

Given: Solid sphere radius R

Formula: Inside g proportional r; outside g proportional 1/r2

Calculation: g increases up to surface then decreases.

Final Answer: At r = R

Exam Tip: Surface is graph peak.

Common Mistake: Do not say centre.

Field Direction

Question: A small test mass is placed near Earth. What is direction of field intensity?

Show Solution

Given: Near Earth

Formula: Field is force per unit mass

Calculation: Attractive force is toward Earth's centre.

Final Answer: Toward Earth's centre

Exam Tip: Field direction is direction of force on test mass.

Common Mistake: Do not say along velocity.

Mass From Field

Question: At distance r, field is g. Find central mass M.

Show Solution

Given: g, r

Formula: g = GM/r2

Calculation: M = gr²/G

Final Answer: gr²/G

Exam Tip: Useful for planetary mass problems.

Common Mistake: Do not forget square on r.

PYQs and Exam-Style Question Bank

Authentic year is not invented. Questions are labelled exam-style when year is not explicitly known.

NEET Exam-style Question 1

Question: For a point mass, gravitational field varies as?

Show Solution

Answer: 1/r².

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept. Use the graph or shell theorem where needed.

NEET Exam-style Question 2

Question: Inside a thin spherical shell, gravitational field is?

Show Solution

Answer: zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

NEET Exam-style Question 3

Question: Inside a uniform solid sphere, g is proportional to?

Show Solution

Answer: r.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Main-style Question 4

Question: The field due to a uniform sphere is maximum at?

Show Solution

Answer: surface.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Main-style Question 5

Question: Binding energy of circular satellite is?

Show Solution

Answer: GMm/2r.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept. Use the graph or shell theorem where needed.

JEE Advanced-style Question 6

Question: For a shell, potential inside is constant; therefore field inside is?

Show Solution

Answer: zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Advanced-style Question 7

Question: If planet radius doubles at same mass, surface field becomes?

Show Solution

Answer: one-fourth.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

CBSE PYQ-style Question 8

Question: Define gravitational field intensity?

Show Solution

Answer: force experienced by unit mass placed at that point.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

A-Level Question 9

Question: Orbital energy is negative for a bound satellite because?

Show Solution

Answer: total energy is less than zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept. Use the graph or shell theorem where needed.

IGCSE Question 10

Question: Gravitational field lines around an isolated mass point?

Show Solution

Answer: toward the mass.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

NEET Exam-style Question 11

Question: For a point mass, gravitational field varies as?

Show Solution

Answer: 1/r².

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

NEET Exam-style Question 12

Question: Inside a thin spherical shell, gravitational field is?

Show Solution

Answer: zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

NEET Exam-style Question 13

Question: Inside a uniform solid sphere, g is proportional to?

Show Solution

Answer: r.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept. Use the graph or shell theorem where needed.

JEE Main-style Question 14

Question: The field due to a uniform sphere is maximum at?

Show Solution

Answer: surface.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Main-style Question 15

Question: Binding energy of circular satellite is?

Show Solution

Answer: GMm/2r.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Advanced-style Question 16

Question: For a shell, potential inside is constant; therefore field inside is?

Show Solution

Answer: zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Advanced-style Question 17

Question: If planet radius doubles at same mass, surface field becomes?

Show Solution

Answer: one-fourth.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept. Use the graph or shell theorem where needed.

CBSE PYQ-style Question 18

Question: Define gravitational field intensity?

Show Solution

Answer: force experienced by unit mass placed at that point.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

A-Level Question 19

Question: Orbital energy is negative for a bound satellite because?

Show Solution

Answer: total energy is less than zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

IGCSE Question 20

Question: Gravitational field lines around an isolated mass point?

Show Solution

Answer: toward the mass.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

NEET Exam-style Question 21

Question: For a point mass, gravitational field varies as?

Show Solution

Answer: 1/r².

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept. Use the graph or shell theorem where needed.

NEET Exam-style Question 22

Question: Inside a thin spherical shell, gravitational field is?

Show Solution

Answer: zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

NEET Exam-style Question 23

Question: Inside a uniform solid sphere, g is proportional to?

Show Solution

Answer: r.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Main-style Question 24

Question: The field due to a uniform sphere is maximum at?

Show Solution

Answer: surface.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Main-style Question 25

Question: Binding energy of circular satellite is?

Show Solution

Answer: GMm/2r.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept. Use the graph or shell theorem where needed.

JEE Advanced-style Question 26

Question: For a shell, potential inside is constant; therefore field inside is?

Show Solution

Answer: zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Advanced-style Question 27

Question: If planet radius doubles at same mass, surface field becomes?

Show Solution

Answer: one-fourth.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

CBSE PYQ-style Question 28

Question: Define gravitational field intensity?

Show Solution

Answer: force experienced by unit mass placed at that point.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

A-Level Question 29

Question: Orbital energy is negative for a bound satellite because?

Show Solution

Answer: total energy is less than zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept. Use the graph or shell theorem where needed.

IGCSE Question 30

Question: Gravitational field lines around an isolated mass point?

Show Solution

Answer: toward the mass.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

NEET Exam-style Question 31

Question: For a point mass, gravitational field varies as?

Show Solution

Answer: 1/r².

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

NEET Exam-style Question 32

Question: Inside a thin spherical shell, gravitational field is?

Show Solution

Answer: zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

NEET Exam-style Question 33

Question: Inside a uniform solid sphere, g is proportional to?

Show Solution

Answer: r.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept. Use the graph or shell theorem where needed.

JEE Main-style Question 34

Question: The field due to a uniform sphere is maximum at?

Show Solution

Answer: surface.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Main-style Question 35

Question: Binding energy of circular satellite is?

Show Solution

Answer: GMm/2r.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

JEE Advanced-style Question 36

Question: For a shell, potential inside is constant; therefore field inside is?

Show Solution

Answer: zero.

Explanation: This follows from gravitational field intensity, sphere theorem, or binding-energy concept.

Common Student Mistakes

Field Direction

Gravitational field points toward the attracting mass, not away from it.

Inside Sphere Formula

Inside a uniform solid sphere, do not use GM/r². Use g = GMr/R³.

Shell vs Solid Sphere

Inside shell g = 0, but inside solid sphere g increases linearly with r.

Binding Energy Sign

Total energy is negative for bound orbit; binding energy is positive magnitude.

Radius Mistake

Use distance from centre for spherical bodies, not height alone.

Graph Peak

For a uniform solid sphere, field is maximum at the surface.

Final Guidance from Kumar Sir

Need help with Gravitation? For Gravitational Field, Sphere/Shell theorem, Binding Energy, NEET/JEE numericals and PYQs, contact Kumar Sir for focused concept clarity and exam practice.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar Sir

Searching for a Physics Tutor? If Gravitational Field, Field Intensity, Binding Energy or NEET/JEE numericals are not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar Sir Visit Website Email Kumar Sir