Question

For a floating body, its weight W and upthrust \[{{\text{F}}_{\text{B}}}\] on it are related as :
A. \[{\text{W > }}{{\text{F}}_{\text{B}}}\]
B. \[{\text{W < }}{{\text{F}}_{\text{B}}}\]
C. \[{\text{W = }}{{\text{F}}_{\text{B}}}\]
D. Nothing can be said

Answer 1

Hint:The basic approach to this question is to understand the relation between the upthrust or buoyant force \[{{\text{F}}_{\text{B}}}\] on a body and its weight W which is given by the ‘law of floatation’, one of the application of the ‘Archimedes’ principle’.

Complete step-by-step answer:
Let us first go through the Archimedes’ principle of fluid mechanics. It states that,
“The upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.”

Mathematically, this law can be given as :
${{\text{F}}_{\text{B}}}\, = \,\,{\text{V}} \times \rho \times {\text{g = Weight of fluid displaced}}$
Where V is the volume of the body submerged in fluid, g is acceleration due to gravity and $\rho $ is the density of the fluid.

Now, according to the ‘law of floatation’, there are three cases,
-When the weight of the body is greater than the buoyant force acting on it \[{\text{W > }}{{\text{F}}_{\text{B}}}\], the body sinks.
-When the weight of the body is equal to the buoyant force acting on it \[{\text{W = }}{{\text{F}}_{\text{B}}}\], the body floats.
-When weight of body is less than the buoyant force acting on it \[{\text{W < }}{{\text{F}}_{\text{B}}}\], then also the body rises until weight becomes equal to buoyant force and finally floats.
So, it can be summarized that the body floats in the fluid if the buoyant force acting on it is greater than or equal to its weight.

(B) and (C) options are correct.

Note:Archimedes’ principle is a law of physics fundamental to fluid mechanics and was formulated by Archimedes and Syracuse. Using this formula, one can also calculate the apparent weight of the body submerged in a fluid and surely force of buoyancy on any body