Gravity Examples in Physics

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=5.97×1024 kgM = 5.97 \times 10^{24} \text{ kg}) and a 1 kg1 \text{ kg} object at Earth's surface (r=6.37×106 mr = 6.37 \times 10^6 \text{ m}). Use G=6.674×10−11 N m2/kg2G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2.

Answer

F≈9.8 NF \approx 9.8 \text{ N}

First step

1
Apply Newton's law of gravitation: F=GMmr2F = \frac{GMm}{r^2}

Full solution

  1. 2
    Substitute: F=6.674×10−11×5.97×1024×1(6.37×106)2F = \frac{6.674 \times 10^{-11} \times 5.97 \times 10^{24} \times 1}{(6.37 \times 10^6)^2}
  2. 3
    Calculate: F=3.98×10144.06×1013≈9.8 NF = \frac{3.98 \times 10^{14}}{4.06 \times 10^{13}} \approx 9.8 \text{ N}
This calculation confirms that g≈9.8 m/s2g \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 seconds3 \text{ seconds}? Ignore air resistance and use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 3

medium
Calculate the gravitational force between two 50 kg50 \text{ kg} masses separated by 2 m2 \text{ m}. Use G=6.674×10−11 N m2/kg2G = 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 s5 \text{ s}. How far does it fall? Use g=9.8 m/s2g = 9.8 \text{ m/s}^2, no air resistance.

Example 6

medium
A satellite orbits at a radius equal to 2RE2 R_E (twice Earth's radius). Compare its gg there to surface gg.

Example 7

hard
How high above Earth's surface does gg drop to 9.0 m/s29.0 \text{ m/s}^2? Take RE=6.37×106 mR_E = 6.37 \times 10^6 \text{ m} and surface g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 8

hard
The Moon orbits Earth at r=3.84×108 mr = 3.84 \times 10^8 \text{ m} with mass 7.35×1022 kg7.35 \times 10^{22} \text{ kg}. Find the gravitational force between Earth (M=5.97×1024 kgM = 5.97 \times 10^{24} \text{ kg}) and the Moon. Use G=6.674×10−11 N m2/kg2G = 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 kg1 \text{ kg} mass equal to 1 N1 \text{ N}? Use G=6.674×10−11 N m2/kg2G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2 and Earth's mass M=5.97×1024 kgM = 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 gg? Earth's radius is R=6.37×106 mR = 6.37 \times 10^6 \text{ m}.

Example 2

medium
What gravitational force exists between two 5 kg5 \text{ kg} masses whose centers are 2 m2 \text{ m} apart? Use G=6.674×10−11 N m2/kg2G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2.

Example 3

easy
Using g=9.8 m/s2g=9.8\text{ m/s}^2, find the gravitational force on a 5 kg5\text{ 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 gg 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
A 2 kg2\text{ kg} object is in free fall (g=9.8g=9.8). Find its acceleration.

Example 10

easy
On the Moon g≈1.6 m/s2g\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 kg10\text{ kg} and a 20 kg20\text{ kg} mass 2 m2\text{ m} apart (G=6.67×10−11G=6.67\times 10^{-11}).

Example 12

medium
An object weighs 80 N80\text{ N} on Earth. At an altitude where gg is one-quarter as strong, find its weight.

Example 13

medium
A ball is dropped from rest (g=10g=10). Find its speed after 3 s3\text{ s}.

Example 14

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

Example 15

medium
Find gg at a planet's surface where a 4 kg4\text{ kg} object weighs 48 N48\text{ N}.

Example 16

medium
Two objects exert 36 N36\text{ N} of mutual gravity. If both masses are doubled (distance fixed), find the new force.

Example 17

challenge
On a planet, a 2 kg2\text{ kg} ball dropped from rest falls 20 m20\text{ m} in 2 s2\text{ s}. Find that planet's gg.

Example 18

challenge
Earth's surface gravity is 9.8 m/s29.8\text{ m/s}^2. At a distance of 22 Earth radii from the center, find gg.

Example 19

challenge
A satellite of mass mm orbits where gravity supplies the centripetal force. At radius rr, show the orbital speed and compute it for glocal=8 m/s2g_{local}=8\text{ m/s}^2, r=5×106 mr=5\times 10^6\text{ m}.

Example 20

medium
A rock dropped from rest falls for 4 s4\text{ s} (g=10g=10). Find the distance fallen.

Example 21

medium
Two 50 kg50\text{ kg} masses are 5 m5\text{ m} apart (G=6.67×10−11G=6.67\times 10^{-11}). Find the gravitational force between them.

Example 22

medium
On a planet, an object weighs 60 N60\text{ N}; its mass is 4 kg4\text{ kg}. Find the planet's gg and the free-fall acceleration there.

Example 23

easy
Find the weight of a 10 kg10 \text{ kg} object near Earth's surface. Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 24

easy
An object weighs 200 N200 \text{ N} on Earth. What is its mass? Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 25

easy
How fast is a freely falling object moving after 4 s4 \text{ s} starting from rest? Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 26

medium
Two 1000 kg1000 \text{ kg} cars are 10 m10 \text{ m} apart. Find the gravitational attraction. Use G=6.674×10−11 N m2/kg2G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2.

Example 27

medium
An astronaut weighs 735 N735 \text{ N} on Earth. What is her weight on the Moon, where gmoon=1.6 m/s2g_{moon} = 1.6 \text{ m/s}^2?

Example 28

medium
Two identical 80 kg80 \text{ kg} people stand 0.5 m0.5 \text{ m} apart. Find the gravitational attraction. Use G=6.674×10−11 N m2/kg2G = 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 gg become?

Example 30

medium
An astronaut weighs 600 N600 \text{ N} on Earth. On a planet where g=24 m/s2g = 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 kg0.5 \text{ kg}, g=9.8 m/s2g = 9.8 \text{ m/s}^2)?

Example 32

medium
A book (1.2 kg1.2 \text{ kg}) is in free fall. What is the net force on it (ignoring air)? Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Example 33

hard
Two stars of mass 2×1030 kg2 \times 10^{30} \text{ kg} each are 1×1011 m1 \times 10^{11} \text{ m} apart. Find the gravitational force between them. Use G=6.674×10−11 N m2/kg2G = 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 gg compared to Earth's.

Example 35

hard
An object falls from rest and reaches the ground at 30 m/s30 \text{ m/s}. From what height was it dropped? Use g=9.8 m/s2g = 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 gg?

Example 37

hard
Two 2.0 kg2.0 \text{ kg} masses at rr apart attract each other with 1.0×10−9 N1.0 \times 10^{-9} \text{ N}. Find rr. Use G=6.674×10−11 N m2/kg2G = 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2.
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Background Knowledge

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

forcemass