The weight of a body in air is 100N. How much will it weigh in water if it displaces 400cm³ of water?

PLEASE READ ALL OF IT, I KNOW IT IS LONG BUT YOU CAN FIND YOUR ANSWER IN THIS

We know that : Density = MASS / VOLUME.
                              Density of water is 1g/cm³ (gram per centimeter cube)

Given : Volume displaced by the water = 400cm³ 
              Weight of the body in air = 100 N 

To Find : The weight of the body in water.

To find the weight of the body in water, first we have to find the buoyant force acting on it.

Answer - Archemedies said that the weight of the water displaced = buoyant force acting on the object.

The Mass of the water displaced can be found out by using the formula Density = Mass/Volume.

1gm/cm³ = Mass / 400cm³ ( We know that the Density of water = 1gm/cm³ and it is given that the volume of water displaced = 400cm³  ).

=> Mass of the displaced water = 400 grams. ( Cross multiplication )

Now we know the mass of water displaced. We have to find out what is the weight of water displaced.                                                                                                                                We know that Weight = mass * acc. due to gravity.

Now as we dont know that the mass of the body is in grams or kilogram, we will take the mass of the body as S.I unit of mass = Kilogram.

In respect to the unit of mass of the body, we will convert 400 gram into kilograoms.
1 kg = 1000 gram
1/1000 kg = 1 gram
400 gram = 2/5 kilogram

We know that 
=> Weight = mass * acc. due to gravity.

=> Weight = 2/5 * 9.8 = 3.92 Newtons.

So the weight of water displaced = 3.92 Newtons.
As archemidies said, the buoyant force acting on an object = weight of the water displaced, therefore the magnitude of buoyant force acting on the object = 3.92 Newtons.

Now since we know the magnitude of the buoyant force acting on the object, we simply subtract the buoyant force from the weight of the object in air to find out it's weight on water.

=> Weight of the object in water = 100 N - 3.92 N = 96.08 Newtons.

Hope this helps,
Regards,
Meherwan
 

PLEASE READ ALL OF IT, I KNOW IT IS LONG BUT YOU CAN FIND YOUR ANSWER IN THIS

We know that : Density = MASS / VOLUME.
                              Density of water is 1g/cm³ (gram per centimeter cube)

Given : Volume displaced by the water = 400cm³ 
              Weight of the body in air = 100 N 

To Find : The weight of the body in water.

To find the weight of the body in water, first we have to find the buoyant force acting on it.

Answer - Archemedies said that the weight of the water displaced = buoyant force acting on the object.

The Mass of the water displaced can be found out by using the formula Density = Mass/Volume.

1gm/cm³ = Mass / 400cm³ ( We know that the Density of water = 1gm/cm³ and it is given that the volume of water displaced = 400cm³  ).

=> Mass of the displaced water = 400 grams. ( Cross multiplication )

Now we know the mass of water displaced. We have to find out what is the weight of water displaced.                                                                                                                                We know that Weight = mass * acc. due to gravity.

Now as we dont know that the mass of the body is in grams or kilogram, we will take the mass of the body as S.I unit of mass = Kilogram.

In respect to the unit of mass of the body, we will convert 400 gram into kilograoms.
1 kg = 1000 gram
1/1000 kg = 1 gram
400 gram = 2/5 kilogram

We know that 
=> Weight = mass * acc. due to gravity.

=> Weight = 2/5 * 9.8 = 3.92 Newtons.

So the weight of water displaced = 3.92 Newtons.
As archemidies said, the buoyant force acting on an object = weight of the water displaced, therefore the magnitude of buoyant force acting on the object = 3.92 Newtons.

Now since we know the magnitude of the buoyant force acting on the object, we simply subtract the buoyant force from the weight of the object in air to find out it's weight on water.

=> Weight of the object in water = 100 N - 3.92 N = 96.08 Newtons.

Hope this helps,
Regards,
Meherwan
 

PLEASE READ ALL OF IT, I KNOW IT IS LONG BUT YOU CAN FIND YOUR ANSWER IN THIS

We know that : Density = MASS / VOLUME.
                              Density of water is 1g/cm³ (gram per centimeter cube)

Given : Volume displaced by the water = 400cm³ 
              Weight of the body in air = 100 N 

To Find : The weight of the body in water.

To find the weight of the body in water, first we have to find the buoyant force acting on it.

Answer - Archemedies said that the weight of the water displaced = buoyant force acting on the object.

The Mass of the water displaced can be found out by using the formula Density = Mass/Volume.

1gm/cm³ = Mass / 400cm³ ( We know that the Density of water = 1gm/cm³ and it is given that the volume of water displaced = 400cm³  ).

=> Mass of the displaced water = 400 grams. ( Cross multiplication )

Now we know the mass of water displaced. We have to find out what is the weight of water displaced.                                                                                                                                We know that Weight = mass * acc. due to gravity.

Now as we dont know that the mass of the body is in grams or kilogram, we will take the mass of the body as S.I unit of mass = Kilogram.

In respect to the unit of mass of the body, we will convert 400 gram into kilograoms.
1 kg = 1000 gram
1/1000 kg = 1 gram
400 gram = 2/5 kilogram

We know that 
=> Weight = mass * acc. due to gravity.

=> Weight = 2/5 * 9.8 = 3.92 Newtons.

So the weight of water displaced = 3.92 Newtons.
As archemidies said, the buoyant force acting on an object = weight of the water displaced, therefore the magnitude of buoyant force acting on the object = 3.92 Newtons.

Now since we know the magnitude of the buoyant force acting on the object, we simply subtract the buoyant force from the weight of the object in air to find out it's weight on water.

=> Weight of the object in water = 100 N - 3.92 N = 96.08 Newtons.

Hope this helps,
Regards,
Meherwan
 

PLEASE READ ALL OF IT, I KNOW IT IS LONG BUT YOU CAN FIND YOUR ANSWER IN THIS

We know that : Density = MASS / VOLUME.
                              Density of water is 1g/cm³ (gram per centimeter cube)

Given : Volume displaced by the water = 400cm³ 
              Weight of the body in air = 100 N 

To Find : The weight of the body in water.

To find the weight of the body in water, first we have to find the buoyant force acting on it.

Answer - Archemedies said that the weight of the water displaced = buoyant force acting on the object.

The Mass of the water displaced can be found out by using the formula Density = Mass/Volume.

1gm/cm³ = Mass / 400cm³ ( We know that the Density of water = 1gm/cm³ and it is given that the volume of water displaced = 400cm³  ).

=> Mass of the displaced water = 400 grams. ( Cross multiplication )

Now we know the mass of water displaced. We have to find out what is the weight of water displaced.                                                                                                                                We know that Weight = mass * acc. due to gravity.

Now as we dont know that the mass of the body is in grams or kilogram, we will take the mass of the body as S.I unit of mass = Kilogram.

In respect to the unit of mass of the body, we will convert 400 gram into kilograoms.
1 kg = 1000 gram
1/1000 kg = 1 gram
400 gram = 2/5 kilogram

We know that 
=> Weight = mass * acc. due to gravity.

=> Weight = 2/5 * 9.8 = 3.92 Newtons.

So the weight of water displaced = 3.92 Newtons.
As archemidies said, the buoyant force acting on an object = weight of the water displaced, therefore the magnitude of buoyant force acting on the object = 3.92 Newtons.

Now since we know the magnitude of the buoyant force acting on the object, we simply subtract the buoyant force from the weight of the object in air to find out it's weight on water.

=> Weight of the object in water = 100 N - 3.92 N = 96.08 Newtons.

Hope this helps,
Regards,
Meherwan
 

PLEASE READ ALL OF IT, I KNOW IT IS LONG BUT YOU CAN FIND YOUR ANSWER IN THIS

We know that : Density = MASS / VOLUME.
                              Density of water is 1g/cm³ (gram per centimeter cube)

Given : Volume displaced by the water = 400cm³ 
              Weight of the body in air = 100 N 

To Find : The weight of the body in water.

To find the weight of the body in water, first we have to find the buoyant force acting on it.

Answer - Archemedies said that the weight of the water displaced = buoyant force acting on the object.

The Mass of the water displaced can be found out by using the formula Density = Mass/Volume.

1gm/cm³ = Mass / 400cm³ ( We know that the Density of water = 1gm/cm³ and it is given that the volume of water displaced = 400cm³  ).

=> Mass of the displaced water = 400 grams. ( Cross multiplication )

Now we know the mass of water displaced. We have to find out what is the weight of water displaced.                                                                                                                                We know that Weight = mass * acc. due to gravity.

Now as we dont know that the mass of the body is in grams or kilogram, we will take the mass of the body as S.I unit of mass = Kilogram.

In respect to the unit of mass of the body, we will convert 400 gram into kilograoms.
1 kg = 1000 gram
1/1000 kg = 1 gram
400 gram = 2/5 kilogram

We know that 
=> Weight = mass * acc. due to gravity.

=> Weight = 2/5 * 9.8 = 3.92 Newtons.

So the weight of water displaced = 3.92 Newtons.
As archemidies said, the buoyant force acting on an object = weight of the water displaced, therefore the magnitude of buoyant force acting on the object = 3.92 Newtons.

Now since we know the magnitude of the buoyant force acting on the object, we simply subtract the buoyant force from the weight of the object in air to find out it's weight on water.

=> Weight of the object in water = 100 N - 3.92 N = 96.08 Newtons.

Hope this helps,
Regards,
Meherwan
 

PLEASE READ ALL OF IT, I KNOW IT IS LONG BUT YOU CAN FIND YOUR ANSWER IN THIS

We know that : Density = MASS / VOLUME.
                              Density of water is 1g/cm³ (gram per centimeter cube)

Given : Volume displaced by the water = 400cm³ 
              Weight of the body in air = 100 N 

To Find : The weight of the body in water.

To find the weight of the body in water, first we have to find the buoyant force acting on it.

Answer - Archemedies said that the weight of the water displaced = buoyant force acting on the object.

The Mass of the water displaced can be found out by using the formula Density = Mass/Volume.

1gm/cm³ = Mass / 400cm³ ( We know that the Density of water = 1gm/cm³ and it is given that the volume of water displaced = 400cm³  ).

=> Mass of the displaced water = 400 grams. ( Cross multiplication )

Now we know the mass of water displaced. We have to find out what is the weight of water displaced.                                                                                                                                We know that Weight = mass * acc. due to gravity.

Now as we dont know that the mass of the body is in grams or kilogram, we will take the mass of the body as S.I unit of mass = Kilogram.

In respect to the unit of mass of the body, we will convert 400 gram into kilograoms.
1 kg = 1000 gram
1/1000 kg = 1 gram
400 gram = 2/5 kilogram

We know that 
=> Weight = mass * acc. due to gravity.

=> Weight = 2/5 * 9.8 = 3.92 Newtons.

So the weight of water displaced = 3.92 Newtons.
As archemidies said, the buoyant force acting on an object = weight of the water displaced, therefore the magnitude of buoyant force acting on the object = 3.92 Newtons.

Now since we know the magnitude of the buoyant force acting on the object, we simply subtract the buoyant force from the weight of the object in air to find out it's weight on water.

=> Weight of the object in water = 100 N - 3.92 N = 96.08 Newtons.

Hope this helps,
Regards,
Meherwan
 

Sorry it got posted so many times.

thanks Meherwan!! :)