Gravitation | Weight of an Object on Moon - Mass and Weight | Class 9 | Science | BYJU'S

Summary

This educational video script explores the nuanced differences between mass and weight, clarifying common misconceptions. It explains that mass, measured in kilograms, is the total amount of matter in an object, while weight, measured in Newtons, is the force exerted by gravity on that mass. The script corrects the common mistake of equating mass with weight by discussing how weighing scales actually measure weight but display it as mass. It also delves into how weight varies with gravity at different locations, such as the poles versus the equator and on other celestial bodies like the Moon. The video aims to provide a clear, concise understanding of these fundamental concepts.

Takeaways

• 🔍 Mass is the total quantity of matter in an object, whereas weight is the force of attraction between the Earth and the object.
• 🌍 People commonly confuse mass and weight because they are often asked for their weight, which is actually their mass.
• 📏 Weighing machines measure weight, but they display the mass by performing an internal calculation using the acceleration due to gravity (G).
• 🌐 The weight of an object varies depending on its location, such as at the poles or the equator, due to differences in gravitational acceleration.
• 🌕 At the poles, where the radius of the Earth is smaller, the gravitational acceleration is higher, resulting in a higher weight compared to the equator.
• 🌌 At the center of the Earth, the net gravitational force on an object is zero, making the weight zero, despite the presence of mass.
• 🌕🌑 The weight on the Moon is approximately one-sixth of the weight on Earth due to the Moon's lower gravitational acceleration.
• 💡 Weightlessness is experienced during free fall because the force acting on a freely falling object is zero, as seen with a ball inside a dropped plastic glass.
• 🏋️‍♂️ A person can lift six times more mass on the Moon than on Earth because the gravitational force on the Moon is one-sixth that of Earth.
• 📈 The concept of 'Concept Bytes' is introduced as a short, crisp, and clear way to learn and understand complex concepts quickly.

Q & A

What is the difference between mass and weight?

Mass is the total quantity of matter in an object, measured in kilograms (kg), while weight is the force exerted on an object due to gravity, measured in Newtons (N).

Why do we often confuse mass and weight?

We often confuse mass and weight because when asked about our weight, we tend to answer in kilograms, which is actually a measure of mass. This confusion arises because weighing machines measure weight but display the reading as if it were mass.

How does the weight of an object vary at different locations on Earth?

The weight of an object varies depending on the location due to differences in the acceleration due to gravity (g). At the equator, the value of g is less due to Earth's larger radius, while at the poles, g is higher, making the weight greater.

What does a weighing machine actually measure?

A weighing machine measures the force of gravity acting on an object, which is the weight. It then internally calculates and displays the mass by dividing the measured weight by the local acceleration due to gravity.

What is the relationship between weight and the acceleration due to gravity?

Weight is calculated as the product of mass and the acceleration due to gravity (W = m * g). Therefore, weight depends on the local value of g, which can vary with location.

Why does the weight of an object become zero when it is in free fall?

When an object is in free fall, it experiences weightlessness because the only force acting on it is gravity, which provides the acceleration needed for free fall. There is no net force acting on the object in the direction of the weighing device, hence the reading is zero.

What is the weight of an object at the center of the Earth?

At the center of the Earth, the net force acting on an object is zero because the gravitational pull from all directions cancels out. Therefore, the weight of an object at the center of the Earth is zero.

How does the acceleration due to gravity on the Moon compare to that on Earth?

The acceleration due to gravity on the Moon is approximately one-sixth of that on Earth, which means an object's weight on the Moon would be one-sixth of its weight on Earth.

If Rahul can lift a maximum of 30 kg on Earth, how much can he lift on the Moon?

Rahul can lift a maximum of 180 kg on the Moon because the Moon's gravity is one-sixth of Earth's. The force he can apply remains the same, but it can support a greater mass due to the reduced gravitational pull.

What would happen to the weight of a gold bar if Amit buys it at the poles and gives it to his friend at the equator?

The weight of the gold bar would decrease when moved from the poles to the equator because the acceleration due to gravity is less at the equator. However, the mass of the gold bar remains constant regardless of location.

Outlines

00:00

🔍 Understanding Mass vs. Weight

The paragraph introduces the common confusion between mass and weight. It explains that while mass is the total quantity of matter in an object, weight is the force of attraction between the Earth and the object. The script clarifies that weighing machines measure weight, not mass, and they provide a mass reading by performing an internal calculation based on the gravitational force. The distinction is important because mass remains constant regardless of location, whereas weight varies with the acceleration due to gravity (G), which changes depending on the location on Earth or other celestial bodies.

05:01

🌍 Gravity's Effect on Weight

This paragraph delves into how the value of gravitational acceleration (G) affects weight. It discusses the variation in G at different points on Earth, such as the equator and the poles, due to the Earth's shape. The script explains that the force of gravity, and consequently weight, is less at the equator and more at the poles. It also touches on the concept of weightlessness during free fall, where an object in free fall experiences zero weight as there is no net force acting on it. The paragraph concludes with a problem-solving example involving spring balances and the weight of an object in different states of motion.

10:02

🌕 Weight on the Moon and Misconceptions

The final paragraph addresses the misconception that weight is greatest at the center of the Earth. It explains that at the center, the net force due to gravity from all directions cancels out, resulting in zero weight. The discussion then shifts to the Moon, where the acceleration due to gravity is one-sixth that of Earth's. A practical example is given to illustrate how much more mass a person could lift on the Moon compared to Earth, given the same force applied. The paragraph ends with a homework question about the weight of gold at different locations on Earth, hinting at the variation in weight due to changes in gravitational acceleration.

Keywords

💡Mass

Mass refers to the total quantity of matter in an object, composed of molecules and atoms. In the video, mass is described as a constant property that does not change regardless of location. It is a fundamental concept in physics and is measured in kilograms (kg). The script clarifies that when people refer to their 'weight' in kilograms, they are actually referring to their mass.

💡Weight

Weight is defined as the force exerted on an object due to gravity. It varies depending on the gravitational pull of the planet or celestial body. The video explains that weight is directly proportional to mass and the acceleration due to gravity (G), expressed by the formula W = mg. It is measured in Newtons, not kilograms, which is a common misconception.

💡Acceleration due to gravity (G)

Acceleration due to gravity is the rate at which an object accelerates toward the center of the Earth (or another celestial body) due to gravity. On Earth, it averages about 9.8 m/s². The video uses this concept to explain how weight varies at different locations on Earth, such as at the equator versus the poles.

💡Weighing Machines

Weighing machines are devices that measure weight. The video clarifies a common misconception by explaining that although weighing machines measure weight, they often display the mass by performing an internal calculation based on the local acceleration due to gravity. This is an important distinction because it shows that what people perceive as their 'weight' on a scale is actually their mass.

💡Equator

The equator is an imaginary line around the Earth's center, equidistant from the poles. The video explains that at the equator, the acceleration due to gravity is slightly less than at the poles because the radius (distance from the center of the Earth) is greater. This results in a slightly lower weight at the equator compared to the poles.

💡Poles

The poles refer to the Earth's northernmost and southernmost points. The video points out that at the poles, the acceleration due to gravity is slightly higher than at the equator, resulting in a slightly higher weight. This is due to the shorter distance from the center of the Earth at these locations.

💡Free Fall

Free fall is the motion of an object under the sole influence of gravity. The video uses the concept of free fall to explain the sensation of weightlessness experienced during free fall, where the weight of an object appears to be zero because it is accelerating downward at the same rate as the force of gravity.

💡Weightlessness

Weightlessness is the feeling of not experiencing the force of gravity. The video explains that in free fall, an object in motion with the acceleration due to gravity experiences weightlessness, as the apparent weight becomes zero. This is demonstrated with the example of a ball inside a plastic glass that remains in place when the glass is dropped.

💡Center of the Earth

The center of the Earth is the core around which the planet is symmetrically arranged. The video clarifies a misconception that at the center of the Earth, an object would experience maximum weight due to the gravitational pull from all directions. However, the net force is zero because the forces cancel each other out, resulting in zero weight.

💡Moon

The Moon is Earth's natural satellite. The video discusses the difference in gravitational pull between Earth and the Moon, stating that the Moon's acceleration due to gravity is approximately one-sixth of Earth's. This is used to illustrate how an object's weight would change when moved from Earth to the Moon.

💡Gold

Gold is a precious metal that is used as an example in the video to discuss the concept of mass constancy. The video poses a question about whether the weight of gold would change when moved from the poles to the equator, highlighting the difference between mass and weight and how mass remains constant while weight varies with location.

Highlights

Definition of mass as the total quantity of matter.

Definition of weight as the force of attraction between Earth and a body.

Weighing machines measure weight and calculate mass through internal calculations.

Weight varies at different locations on Earth due to differences in gravitational acceleration.

At the equator, the value of gravitational acceleration (g) is less, resulting in a lower weight.

At the poles, the value of g is higher, resulting in a higher weight.

Mass remains constant regardless of location, while weight changes with gravitational acceleration.

Weightlessness is experienced during free fall as the force of gravity is balanced by the acceleration of the body.

At the center of the Earth, the net gravitational force is zero, resulting in zero weight.

On the Moon, the acceleration due to gravity is one-sixth of Earth's, making weight six times less.

Rahul can lift six times more mass on the Moon due to its lower gravitational acceleration.

The misconception that weight is maximum at the center of the Earth is debunked.

The formula for weight is mass times gravitational acceleration (W = mg).

The SI unit for mass is kilograms (kg), while for weight, it is Newtons (N).

A weight of 100 Newtons attached to two spring balances will show different readings depending on whether they are at rest or in free fall.

Amit's friend will not agree with the weight of the gold bot at the equator due to the difference in gravitational acceleration.

The concept of 'Concept Bytes' is introduced as a short, crisp, and clear way of learning.

Transcripts

[Music]

foreign

let me ask you something what is the

difference between mass and weight I

know the first time you hear this

question you feel like what kind of

silly question is this mass is mass is

the total quantity of matter where it is

weight it's the force

but let me tell you from where this

confusion starts what if somebody asked

you what's your weight what do you

answer

40 kg 30 kg 50 kg

you answer in kgs right

if you also have this confusion what do

weighing machines measure what do they

tell you is it mass is it weight welcome

to the short under 10 minute session we

call as the concept bytes in today's

session I'll tell you the exact

difference between mass and weight what

do the weighing machines tell you what

is it I'll tell you that and apart from

that we'll discuss everything about wage

how the weight varies at different

different positions if you go inside the

earth if you go different planets if you

go to the Moon right we'll solve some

questions nice short crisp and clear

that's what we call as concert bytes

welcome if you know what we do press the

like button because this video is going

to be awesome all right let's start

so if somebody asks you do mass and

weight refer to the same thing so let's

say this person he's saying now I'm fit

my weight is showing 70 kg she say 70 is

not your weight here it's your mass

so why do we always answer in kgs

let me tell you exact difference between

mass and weight see we all know this

mass is the total quantity of matter

right how much of matter what is matter

molecules atoms whatever it is

what is it made up of total quantity of

matter is called as the mass all right

what is weight weight is the force of

attraction right it is the force of

attraction between Earth and the body at

least on Earth we are talking about or

the planet could be right between any

planet or any Heavenly Body and the

masses

that is your weight right and what is

your mass it is the total quantity of

matter in you correct so and the mass it

does not depend on G Master total

quantity of matter is

so it does not depend on G which means

it does not depend on acceleration due

to gravity but weight depends on G why

weight is mass into acceleration due to

gravity this formula is not different it

is f equals m a only weight is the force

force force equals mass into its

acceleration on Earth we call the force

as weight we call as acceleration

gravitational acceleration to gravity

and I have cable term so w equals mg

that's how this formula came with same

formula right so it depends on G mass is

in kgs right its s i unit is kgs but

weight being Force has the s i unit of

force which is Newton it always remains

constant mass does not change by you

know mass is not changed until unless

you start moving the speed of light

it varies from place to place right

weight varies from place to place and

yes it does

it can never be zero Mass cannot be zero

it can be zero at the center of the

earth what

I'll tell you what and why this

misconception comes I'll tell you that

so no

let's do this first question rho anyway

600 Newton at a point near the equator

if she measures her weight at the North

Pole her weight will

come on we have done this we have done

this

if she measures her weight at North Pole

her weight will compare to 600 Newton

which is measured at equator

well

W equals m into G right now the value of

G is an average value of 9.8 but we have

learned this that on the equator the

distance of the body from the center is

more why because the radius of Earth

equator is more Earth is not a perfect

circle it's a geoid shape right so at

the Equator the radius is more compared

to the poles now what is g g equals g m

upon R square if this radius is more G

will be less so at Equator the value of

acceleration due to gravity is less

means the weight is going to be less at

the poles the value of G is going to be

moved that is acceleration due to

gravity is going to be more it is about

9.83 means your weight will be more if

you want to lose weight and you live

near poles come to Equator your weight

will be you know less all right okay so

weight is M into G and G is remember R

square which means at the Equator the

value of G is less polar radius is less

than equatorial radius so her weight

will be more if she goes to the pole why

because value of G is more at the post

right so her weight will in increase

Mass into G at poles is going to be more

than Mass into GF equator okay fine now

let me come back to the initial question

if mass is different and weight is

different then what is it that the

weighing machines measure

weighing machines they measure your

weight only

they measure your weight only yes but

what else

they tell you the value of the mass by

doing internal calculation by if think

about it m into G if somebody measures

and you divide it with G what it becomes

it becomes Mass right so they answer it

like Mass but they actually measure mass

into G right mg if I go to class 11 I

would probably end up saying they

measure the normal force but right now

I'm just telling you okay they measure

your weight only they measure your

weight but they divide it with the value

of G to give you their Mass so they are

answering in terms of mass but they are

measuring weight right clear fine okay

a weight of 100 Newton is attached to

the end of two spring balances A and B

the spring balance a is attached to

ceiling and B is allowed to fall freely

find the readings of A and B

respectively

B is in free fall and a is hanging

nicely spring balances can tell you what

is the force right if you hang a hundred

Newton if you know the answer come on

think about it pause the video think

about it and then cross checker

weight of 100 Newton attached to the end

of two spring balances by a is at rest

we all know if I take a spring balance I

keep it at rest and hang a mass it will

read the weight of the mass right so a

should be 100 Newton we all know that

what about B

what do you think will be measure and B

is really falling

have you noticed whenever you fall

freely

we say it is weightlessness Hannah

correct you feel weightlessness when you

fall right correct so with the same

logic you can say when a body is freely

falling it weights becomes zero its

weight becomes zero means the force

becomes zero means the spring balance

will read zero you can try it you can

try this one it's very easy you know you

can take a bottle you can uh or you can

say take a glass

which class would you say take a plastic

glass take a plastic glass and put a

ball inside it and you drop it you will

see the ball will remain at its position

okay fine so it will be 100 Newton and

zero so when a body falls it experiences

weightlessness if a body falls freely

means with the acceleration due to

gravity the weight becomes zero correct

fine but yeah so it is 100 and 0 Newton

now let me ask you what is the weight at

the center of foreign

but let me tell you people don't believe

that a lot of people have this confusion

why

listen weight equals m into g means M

into g m by r

square right

M into g m by R square correct answer

if radius at equator is more the value

of G is less if the radius at pole is

less the value of G is more agreed by

pole pay radius

what is g acceleration due to gravity

you know

if we take the body inside the earth

means the value of G will be even lesser

does it mean the weight will be even

more which means if I take the body to

the center means radius is 0 weight

would be infinite is it no

first of all why was this Force

occurring because the mass was pulling

you know because of the force of

gravitational

foreign

imagine you are at the center and from

all the directions people are pulling

you with the Rope okay imagine this

scenario okay you are standing at the

center and from every direction

you are being pulled by a rope okay you

are being pulled in each and every

direction by a rope

what is the net force on you think about

it come on what is the net force on you

zero why because you are being pulled

from every direction

correct so what is happening when you're

at the center of the earth the mass of

the Earth around this body is pulling

this body in all the directions in all

the direction it is being pulled so net

force becomes zero if Force becomes zero

weight becomes zero so that is why

we always think that we feel maximum

weight at the center of Earth but it's a

misconception actually wait at the

center of Earth is zero clear it's a

very important very basic question but

very commonly occurring questions okay a

weight on the moon

acceleration to gravity of the Moon I

gave you this homework in a previous

video if you remember I think you might

have solved it right so

the gravity the acceleration due to

gravity on moon is G by 6.

means the weight will be weight of the

earth divided by 6 correct if G is 1 by

6 weight will also be one by six now

six times weaker right so G Dash is the

acceleration of gravity on the moon and

G is the action derivative of Earth so

acceleration due to gravity on the moon

GM is equal to 1.6 meter per second

Square do you have to remember the value

no but 1 by 6 is something I want you to

remember okay

so let's do a very quick question the

maximum mass that Rahul can lift on the

earth is 30 kg what will be the maximum

mass that he can lift on the moon

and you apply the same John the same

Force how much mass can he lift that is

the question if you know the answer or

if you can solve this question pause it

and solve it otherwise cross check

Ticket listen to me I told you

Rahul has the same amount of force he

can apply so on Earth how much force is

he applying on Earth he is applying

Force which is the weight of the body W

is equal to 30 into

G of earth right okay when he goes to

Moon he can apply the same Force huh

okay so he is applying Force which is 30

into GE and it will be equal to how much

mass he can lift multiplied by the

acceleration to gravity on the moon

what have I done

I have equated the force the force he

can apply on Earth is equal to the force

he can apply on moon right correct

is equal to how much mass correct or you

can say the force he is applying is

equal to how much of the weight weight

so 30 into G is equal to M into g m so I

can say 30 into GE is equal to M into g

e By 6 y because G of moon is equal to 1

by 6 of G of Earth so G is a g e cancel

mass will be 30 into 6 is equal to

180 kgs so on moon he can lift 1 80 kgs

six times

if imagine imagine right if on Earth

the gravity is more means you can lift a

small Mass but you have that much force

right and that much force will be equal

to a greater mass on moon the moon's

gravity is 1 6 means you can lift any

Mass which is six times heavier on the

moon henna take it fine clear so that's

why 180 kgs becomes the correct answer

all right ah a small homework question

for all of you Amit buys few grams of

gold at the poles as per the instruction

of one of his friends he hands over the

same when he meets him at the equator

will the friend agree with the height of

gold bot sorry weight of the gold bot if

not why it's your ncert equation by the

way come on if you know the answer tell

me in the comment section otherwise

others will

give you the answer all right everybody

with this I want all of you to try this

question tell me in the comment section

and I hope you like this short crisp and

clear way of learning because as the

concept bites we'll do live questions

we'll do practice questions a lot but

this is a time saving way I want all of

you to study like this if you think this

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don't forget and see you next time take

care bye