Question

Fill in the blank.
A ball and a cube of the same material are fully immersed in a liquid. Both will experience ________ _ buoyant force.
A) Same
B) Different
C) Both A and B
D) None

Answer 1

In order to solve this question we should know about the concept of buoyant force. Buoyant force depends on the volume of the objects immersed in the liquid and not on the material of the objects immersed in the liquid.

Formula Used:
${F_B} = {V_{immersed}}\rho g$
Here, ${F_B}$ is the buoyant force experienced by the object immersed in the liquid. This force is applied by the liquid.
${V_{immersed}}$ is the volume of the object immersed in the liquid
$\rho$ is the density of the liquid in which the object is immersed
$g$ is the acceleration due to gravity.

Complete Step by Step Solution:
When an object is immersed in a liquid the pressure exerted by the fluid or the hydrostatic pressure, is the pressure in an equilibrium system that depends on the density of the fluid, acceleration due to gravity and the volume of the immersed object in the liquid. This pressure can also be said in terms of the buoyant force applied by the liquid on the material immersed.
Here, in this question a ball and a cube are immersed.

Yet the material of both the objects is the same but the point to ponder here is that both have different volumes.

We know that, according to the Archimedes Principle, the magnitude of buoyant force that is experienced by the object immersed in the liquid is equal to the weight of liquid displaced by it by being placed in it and also its magnitude does not depend upon the nature and material of the objects.
The expression for the Buoyant Force is given by,
${F_B} = {V_{immersed}}\rho g$
Here, $\rho$ and $g$ are constants.
Hence the buoyant force is dependent only on the volume immersed in the liquid.
So, ${F_B}\propto {V_{immersed}}$

As the volume for the cube and ball is different, so even if they are made up of the same material, they will displace different volumes of liquids and hence will experience different buoyant forces.

So, option B is the correct answer.

Note: As we know, Archimedes’ Principle helps us to calculate the buoyancy of any floating object or partially or fully immersed liquid. The downward force applied on the liquid is simply due to its weight while the upward experienced by the object is the buoyant force applied by the liquid on the object.