
The apparent weight of the body in a liquid is
A)
B)
C)
D) None of these.
Answer
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Hint:Whenever a body is submerged partially or fully in a liquid it experiences an upthrust. The weight of the body is felt to decrease under the action of the upthrust. Archimedes’ principle gives the apparent weight of the body to be equal to the difference between the weight of the body and the upthrust experienced by it.
Formulas used:
-The apparent weight of a body in a liquid is given by, where is the weight of the body and is the force of buoyancy or upthrust experienced by the body.
-The weight of a body is given by, where is the volume of the body, is the density of the body and is the acceleration due to gravity.
-The upthrust on a body by a liquid is given by, where is the volume of the displaced liquid, is the density of the liquid and is the acceleration due to gravity.
Complete step by step answer.
Step 1: Sketch a figure representing a body in liquid.
The above figure depicts a body immersed in some liquid. (It can be partially or fully immersed)
The force of buoyancy or upthrust is directed upwards and the weight of the body is directed downwards.
Let be the volume and be the density of the body and be the density of the liquid.
Step 2: Based on Archimedes’ principle, express the apparent weight of the body.
The weight of the body can be expressed as ----------- (1).
The upthrust experienced by the body can be expressed as --------- (2).
According to Archimedes’ principle, the upthrust acting on the body will be equal to the weight of the body. So the difference between the weight and the upthrust will correspond to the apparent weight of the body.
i.e., ------ (3)
Substituting equations (1) and (2) in (3) we get,
So the correct option is A.
Note: The volume of the liquid displaced on immersing the body will be equal to the volume of the body. The mass of an object is expressed as where is the volume of the object and is its density. Since the weight of an object is usually expressed as , substituting in the relation for the weight we get, as equation (1).
Formulas used:
-The apparent weight of a body in a liquid is given by,
-The weight of a body is given by,
-The upthrust on a body by a liquid is given by,
Complete step by step answer.
Step 1: Sketch a figure representing a body in liquid.

The above figure depicts a body immersed in some liquid. (It can be partially or fully immersed)
The force of buoyancy or upthrust
Let
Step 2: Based on Archimedes’ principle, express the apparent weight of the body.
The weight of the body can be expressed as
The upthrust experienced by the body can be expressed as
According to Archimedes’ principle, the upthrust acting on the body will be equal to the weight of the body. So the difference between the weight and the upthrust will correspond to the apparent weight of the body.
i.e.,
Substituting equations (1) and (2) in (3) we get,
So the correct option is A.
Note: The volume of the liquid displaced on immersing the body will be equal to the volume of the body. The mass of an object is expressed as
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