A Bucket of Water Feels Lighter While It Is Still in the Well
Learn why mass and weight are different quantities, calculate weight in newtons from a given mass, compare upthrust with weight to decide floating or sinking, and explain why immersed objects feel lighter.
Why does a bucket of water feel lighter while it is still in the well?
Because the water pushes upward on it. That upward push is called upthrust or buoyant force, and it takes part of the bucket's weight off your hands.
Lift the bucket clear of the water and the upthrust vanishes, so the full weight returns at once. This page covers everything in the CBSE Class 8 Science chapter's second part: mass against weight, calculating weight, upthrust, and floating and sinking.
Lift the bucket clear of the water and the upthrust vanishes, so the full weight returns at once. This page covers everything in the CBSE Class 8 Science chapter's second part: mass against weight, calculating weight, upthrust, and floating and sinking.
What is the difference between mass and weight?
Mass is the quantity of matter in a body. Weight is the force with which the Earth attracts that body.
They differ in every respect that matters:
- Mass — measured in kilograms (kg), using a beam balance. It is the same everywhere, because the amount of matter does not change.
- Weight — measured in newtons (N), using a spring balance. It changes with location, because it depends on the strength of gravity.
So a bag of rice with a mass of 5 kg has a mass of 5 kg in Delhi, on a mountain top or on the Moon. Its weight, however, is about one-sixth as much on the Moon, because the Moon's gravitational pull is weaker.
Weight is a force, so it has a direction — always vertically downward, towards the centre of the Earth.
Everyday speech blurs this, and the syllabus does not. A shopkeeper saying "two kilos of weight" is really stating a mass, because a beam balance compares masses. Strictly, mass is in kilograms and weight is in newtons, and a question asking for weight expects newtons.
They differ in every respect that matters:
- Mass — measured in kilograms (kg), using a beam balance. It is the same everywhere, because the amount of matter does not change.
- Weight — measured in newtons (N), using a spring balance. It changes with location, because it depends on the strength of gravity.
So a bag of rice with a mass of 5 kg has a mass of 5 kg in Delhi, on a mountain top or on the Moon. Its weight, however, is about one-sixth as much on the Moon, because the Moon's gravitational pull is weaker.
Weight is a force, so it has a direction — always vertically downward, towards the centre of the Earth.
Everyday speech blurs this, and the syllabus does not. A shopkeeper saying "two kilos of weight" is really stating a mass, because a beam balance compares masses. Strictly, mass is in kilograms and weight is in newtons, and a question asking for weight expects newtons.
Formula
How do you calculate the weight of a given mass?
Weight is mass multiplied by the acceleration due to gravity:
where is the mass in kilograms, is about on Earth, and comes out in newtons.
Worked examples.
A bag of mass :
A book of mass . Convert to kilograms first, since :
A student of mass :
Running it backwards. An object weighs , so its mass is
A spring balance measures weight directly. It contains a spring that stretches in proportion to the force pulling it, and a pointer moves along a scale marked in newtons. Hang the object from the hook, let it come to rest, and read the value at eye level.
The conversion to kilograms is the step that decides the answer. Using instead of gives — the weight of a small car rather than a school book, and an answer any sense check would reject.
where is the mass in kilograms, is about on Earth, and comes out in newtons.
Worked examples.
A bag of mass :
A book of mass . Convert to kilograms first, since :
A student of mass :
Running it backwards. An object weighs , so its mass is
A spring balance measures weight directly. It contains a spring that stretches in proportion to the force pulling it, and a pointer moves along a scale marked in newtons. Hang the object from the hook, let it come to rest, and read the value at eye level.
The conversion to kilograms is the step that decides the answer. Using instead of gives — the weight of a small car rather than a school book, and an answer any sense check would reject.
How does upthrust decide whether something floats or sinks?
Two forces act on an object in a liquid: its weight pulling it down, and the upthrust pushing it up. Comparing them settles the outcome.
- Upthrust less than weight — the object sinks. An iron nail, a stone, a coin.
- Upthrust equal to weight — the object floats, resting in balance. A cork, a piece of wood, a plastic ball.
- Upthrust greater than weight — the object is pushed up until enough of it rises above the surface for the two to balance.
Upthrust exists because a liquid exerts pressure on everything in it, and that pressure is greater lower down. The push upward on the object's base therefore exceeds the push downward on its top, and the difference is the upthrust.
It follows that upthrust depends on:
- The volume of the object immersed — more of it under water means more upthrust
- The density of the liquid — a denser liquid gives a bigger push
Anyone who has tried to hold an empty plastic bottle under water has felt the upthrust pushing back hard.
That second factor explains a result students find odd. An egg that sinks in plain water will float in strongly salted water, because salt water is denser and supplies more upthrust — the egg has not changed at all, only the liquid has.
- Upthrust less than weight — the object sinks. An iron nail, a stone, a coin.
- Upthrust equal to weight — the object floats, resting in balance. A cork, a piece of wood, a plastic ball.
- Upthrust greater than weight — the object is pushed up until enough of it rises above the surface for the two to balance.
Upthrust exists because a liquid exerts pressure on everything in it, and that pressure is greater lower down. The push upward on the object's base therefore exceeds the push downward on its top, and the difference is the upthrust.
It follows that upthrust depends on:
- The volume of the object immersed — more of it under water means more upthrust
- The density of the liquid — a denser liquid gives a bigger push
Anyone who has tried to hold an empty plastic bottle under water has felt the upthrust pushing back hard.
That second factor explains a result students find odd. An egg that sinks in plain water will float in strongly salted water, because salt water is denser and supplies more upthrust — the egg has not changed at all, only the liquid has.
Why does an iron ship float when an iron nail sinks?
Because a ship is mostly hollow. Its hull encloses a large volume of air, so the ship as a whole displaces a great deal of water and receives an upthrust equal to its weight. A solid nail of the same metal displaces almost nothing and sinks.
So the question is never "how heavy is it?" but how heavy is it for its volume — which is its density.
Against water:
- Floats — cork, wood, plastic ball, ice, oil, a sealed empty bottle
- Sinks — iron nail, stone, coin, glass marble, sand
Comparing densities gives the same answer as comparing forces. An object less dense than the liquid floats; one more dense sinks.
Ice floating matters beyond the classroom: because solid water is less dense than liquid water, ice forms a layer on top of a pond instead of sinking, and fish survive beneath it.
And the feeling lighter effect now has a number. A stone of weight that experiences an upthrust of when immersed has an apparent weight of
A spring balance would read while the stone hangs in the water and once lifted out.
Note what has not changed: the stone's mass and its actual weight are the same throughout. Only the apparent weight is reduced, because the upthrust takes part of the load — which is exactly why letting water into a ship's hull makes it sink.
So the question is never "how heavy is it?" but how heavy is it for its volume — which is its density.
Against water:
- Floats — cork, wood, plastic ball, ice, oil, a sealed empty bottle
- Sinks — iron nail, stone, coin, glass marble, sand
Comparing densities gives the same answer as comparing forces. An object less dense than the liquid floats; one more dense sinks.
Ice floating matters beyond the classroom: because solid water is less dense than liquid water, ice forms a layer on top of a pond instead of sinking, and fish survive beneath it.
And the feeling lighter effect now has a number. A stone of weight that experiences an upthrust of when immersed has an apparent weight of
A spring balance would read while the stone hangs in the water and once lifted out.
Note what has not changed: the stone's mass and its actual weight are the same throughout. Only the apparent weight is reduced, because the upthrust takes part of the load — which is exactly why letting water into a ship's hull makes it sink.
Exam tip
Exam tip: converting grams to kilograms before using W = mg
Weight questions lose marks in the same two places every time.
Convert the mass to kilograms on its own line before substituting — ** — then use with .
Give mass in kg and weight in N, never the other way round. An answer of "weight kg" is marked wrong even where the number is right.
When asked about the Moon, say the mass stays the same and the weight becomes about one-sixth, and give the reason as weaker gravity.
For floating and sinking, compare upthrust with weight, or compare densities — and state which comparison you used.
And for apparent weight, show the subtraction: *apparent weight actual weight upthrust*, noting that the real weight is unchanged.
Convert the mass to kilograms on its own line before substituting — ** — then use with .
Give mass in kg and weight in N, never the other way round. An answer of "weight kg" is marked wrong even where the number is right.
When asked about the Moon, say the mass stays the same and the weight becomes about one-sixth, and give the reason as weaker gravity.
For floating and sinking, compare upthrust with weight, or compare densities — and state which comparison you used.
And for apparent weight, show the subtraction: *apparent weight actual weight upthrust*, noting that the real weight is unchanged.
Did you know
Why does an egg float in salty water but sink in plain water?
Because adding salt makes the water denser, and a denser liquid pushes up harder.
In plain water the upthrust on the egg is less than the egg's weight, so it sinks. Stir in several spoons of salt and the same volume of liquid now contains more matter, so the upthrust on the egg increases. Once it matches the egg's weight, the egg rises and floats.
The egg is unchanged throughout — same mass, same volume, same weight. Only the liquid changed, which is a neat reminder that floating is never a property of an object alone but of the pair: the object and the liquid it sits in.
In plain water the upthrust on the egg is less than the egg's weight, so it sinks. Stir in several spoons of salt and the same volume of liquid now contains more matter, so the upthrust on the egg increases. Once it matches the egg's weight, the egg rises and floats.
The egg is unchanged throughout — same mass, same volume, same weight. Only the liquid changed, which is a neat reminder that floating is never a property of an object alone but of the pair: the object and the liquid it sits in.
Key takeaways
Mass, weight and upthrust: quick revision
- Mass is the quantity of matter in kilograms, measured on a beam balance, and it is the same everywhere. Weight is the Earth's pull in newtons, measured on a spring balance, and it changes with gravity.
- with , so weighs and weighs — convert to kg first.
- On the Moon the mass is unchanged while the weight is about one-sixth.
- Upthrust is the upward push of a liquid, arising because liquid pressure is greater lower down; it increases with the volume immersed and the liquid's density.
- Upthrust less than weight means sink, equal means float — which is the same as saying a body less dense than the liquid floats.
- A hollow ship floats because its trapped air lowers its overall density, and apparent weight actual weight upthrust, with the real weight unchanged.
You will remember all of this far better after answering five questions on it than after reading it twice.
- with , so weighs and weighs — convert to kg first.
- On the Moon the mass is unchanged while the weight is about one-sixth.
- Upthrust is the upward push of a liquid, arising because liquid pressure is greater lower down; it increases with the volume immersed and the liquid's density.
- Upthrust less than weight means sink, equal means float — which is the same as saying a body less dense than the liquid floats.
- A hollow ship floats because its trapped air lowers its overall density, and apparent weight actual weight upthrust, with the real weight unchanged.
You will remember all of this far better after answering five questions on it than after reading it twice.