Gravity Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Gravity.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The universal attractive force between any two objects with mass, decreasing with the square of distance.

Everything pulls on everything else—but only huge things (like Earth) pull noticeably.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Gravity asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to gravity but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Free Body Diagrams Mistakes

Worked Examples

Example 1

easy

Calculate the gravitational force between Earth (

M = 5.97 \times 10^{24} \text{ kg}

) and a

1 \text{ kg}

object at Earth's surface (

r = 6.37 \times 10^6 \text{ m}

). Use

G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2

Answer

F \approx 9.8 N

First step

Apply Newton's law of gravitation:

F = \frac{G M m}{r^{2}}

Full solution

2
Substitute: $F = \frac{6.674 \times 10^{- 11} \times 5.97 \times 10^{24} \times 1}{(6.37 \times 10^{6})^{2}}$
3
Calculate: $F = \frac{3.98 \times 10^{14}}{4.06 \times 10^{13}} \approx 9.8 N$

This calculation confirms that

g \approx 9.8 \text{ m/s}^2

at Earth's surface. Gravity is the attractive force between any two masses, governed by the universal law of gravitation.

Example 2

easy

A ball is dropped from rest near Earth's surface. How fast is it going after

3 \text{ seconds}

? Ignore air resistance and use

g = 9.8 \text{ m/s}^2

Example 3

medium

Calculate the gravitational force between two

50 \text{ kg}

masses separated by

2 \text{ m}

. Use

G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2

Example 4

medium

If the distance between two masses triples, by what factor does the gravitational force change?

Example 5

medium

A rock is dropped from rest and falls for

5 \text{ s}

. How far does it fall? Use

g = 9.8 \text{ m/s}^2

, no air resistance.

Example 6

medium

A satellite orbits at a radius equal to

2 R_E

(twice Earth's radius). Compare its

g

there to surface

g

Example 7

hard

How high above Earth's surface does

g

drop to

9.0 \text{ m/s}^2

? Take

R_E = 6.37 \times 10^6 \text{ m}

and surface

g = 9.8 \text{ m/s}^2

Example 8

hard

The Moon orbits Earth at

r = 3.84 \times 10^8 \text{ m}

with mass

7.35 \times 10^{22} \text{ kg}

. Find the gravitational force between Earth (

M = 5.97 \times 10^{24} \text{ kg}

) and the Moon. Use

G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2

Example 9

challenge

At what distance from Earth's center is the gravitational force on a

1 \text{ kg}

mass equal to

1 \text{ N}

? Use

G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2

and Earth's mass

M = 5.97 \times 10^{24} \text{ kg}

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

At what height above Earth's surface would the gravitational acceleration be half of

g

? Earth's radius is

R = 6.37 \times 10^6 \text{ m}

Example 2

medium

What gravitational force exists between two

5 \text{ kg}

masses whose centers are

2 \text{ m}

apart? Use

G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2

Example 3

easy

Using

g=9.8\text{ m/s}^2

, find the gravitational force on a

5\text{ kg}

mass at Earth's surface.

Gravitational force on a 5 kg mass at Earth's surface

Example 4

easy

Does gravitational force increase or decrease as two objects move farther apart?

Example 5

easy

What does the symbol

g

represent near Earth's surface?

Example 6

easy

If the distance between two masses doubles, by what factor does gravity change?

Example 7

easy

Do all objects in free fall (no air resistance) accelerate at the same rate?

Example 8

easy

Is gravity a contact force or a non-contact (field) force?

Example 9

easy

2\text{ kg}

object is in free fall (

g=9.8

). Find its acceleration.

Example 10

easy

On the Moon

g\approx 1.6\text{ m/s}^2

. Compared with Earth, is the free-fall acceleration larger or smaller?

Example 11

medium

Find the gravitational force between a

10\text{ kg}

and a

20\text{ kg}

mass

2\text{ m}

apart (

G=6.67\times 10^{-11}

Example 12

medium

An object weighs

80\text{ N}

on Earth. At an altitude where

g

is one-quarter as strong, find its weight.

Example 13

medium

A ball is dropped from rest (

g=10

). Find its speed after

3\text{ s}

Example 14

medium

Compare the gravitational forces if the distance between two masses is tripled.

Example 15

medium

Find

g

at a planet's surface where a

4\text{ kg}

object weighs

48\text{ N}

Example 16

medium

Two objects exert

36\text{ N}

of mutual gravity. If both masses are doubled (distance fixed), find the new force.

Example 17

challenge

On a planet, a

2\text{ kg}

ball dropped from rest falls

20\text{ m}

2\text{ s}

. Find that planet's

g

Example 18

challenge

Earth's surface gravity is

9.8\text{ m/s}^2

. At a distance of

2

Earth radii from the center, find

g

Example 19

challenge

A satellite of mass

m

orbits where gravity supplies the centripetal force. At radius

r

, show the orbital speed and compute it for

g_{local}=8\text{ m/s}^2

r=5\times 10^6\text{ m}

Example 20

medium

A rock dropped from rest falls for

4\text{ s}

(

g=10

). Find the distance fallen.

Example 21

medium

Two

50\text{ kg}

masses are

5\text{ m}

apart (

G=6.67\times 10^{-11}

). Find the gravitational force between them.

Example 22

medium

On a planet, an object weighs

60\text{ N}

; its mass is

4\text{ kg}

. Find the planet's

g

and the free-fall acceleration there.

Example 23

easy

Find the weight of a

10 \text{ kg}

object near Earth's surface. Use

g = 9.8 \text{ m/s}^2

10 kg block at rest on Earth's surface

Example 24

easy

An object weighs

200 \text{ N}

on Earth. What is its mass? Use

g = 9.8 \text{ m/s}^2

Example 25

easy

How fast is a freely falling object moving after

4 \text{ s}

starting from rest? Use

g = 9.8 \text{ m/s}^2

Example 26

medium

Two

1000 \text{ kg}

cars are

10 \text{ m}

apart. Find the gravitational attraction. Use

G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2

Example 27

medium

An astronaut weighs

735 \text{ N}

on Earth. What is her weight on the Moon, where

g_{moon} = 1.6 \text{ m/s}^2

Astronaut on the Moon surface — weight is about 1/6 of Earth weight

Example 28

medium

Two identical

80 \text{ kg}

people stand

0.5 \text{ m}

apart. Find the gravitational attraction. Use

G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2

Example 29

medium

If Earth's mass were doubled but its radius stayed the same, what would

g

become?

Example 30

medium

An astronaut weighs

600 \text{ N}

on Earth. On a planet where

g = 24 \text{ m/s}^2

, what is her weight?

Example 31

medium

A ball is thrown upward and rises to a peak. At the peak, what is the gravitational force on it (mass

0.5 \text{ kg}

g = 9.8 \text{ m/s}^2

Ball at the peak of its throw — weight still acts downward

Example 32

medium

A book (

1.2 \text{ kg}

) is in free fall. What is the net force on it (ignoring air)? Use

g = 9.8 \text{ m/s}^2

Book in free fall — net force equals weight

Example 33

hard

Two stars of mass

2 \times 10^{30} \text{ kg}

each are

1 \times 10^{11} \text{ m}

apart. Find the gravitational force between them. Use

G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2

Example 34

hard

A planet has twice Earth's mass and three times Earth's radius. Find its surface

g

compared to Earth's.

Example 35

hard

An object falls from rest and reaches the ground at

30 \text{ m/s}

. From what height was it dropped? Use

g = 9.8 \text{ m/s}^2

, no air resistance.

Example 36

hard

If a planet's radius shrinks to half its current value but its mass stays the same, what happens to surface

g

Example 37

hard

Two

2.0 \text{ kg}

masses at

r

apart attract each other with

1.0 \times 10^{-9} \text{ N}

. Find

r

. Use

G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2

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Related Concepts

Force Mass Weight Orbital Motion Gravitational Field

Background Knowledge

These ideas may be useful before you work through the harder examples.

forcemass