Question

An Aluminum Sphere is dipped into water at 10°C. If the temperature is increased, the force of buoyancy,
(A) Will increase
(B) Will decrease
(C) Will remain Constant
(D) May increase or decrease, depending on the radius of the sphere.

Answer 1

Hint To answer this question, we have to look at the effect of temperature at the molecular level. Then using the phenomenon of convection, and Boyle's law we can get the final answer.

Formula Used: The formula used in this solution is given as,
$\Rightarrow {F_B} = \rho gV$
Here, ${F_B}$ is the force of buoyancy, $\rho $ is the density of the liquid, $g$ is the acceleration due to gravity, and $V$ is the volume of the body immersed in the liquid.

Complete step by step answer
We will first try to understand the motion of water molecules on gaining temperature. On increasing the temperature, the molecules will gain energy that will be of kinetic nature. This will make the molecules move rapidly, which will set convection currents in the liquid. The phenomenon of convection will make the hotter layer to rise upwards and the cooler layer to move down. Thus, the layer below the body will rise upwards on heating which will increase in turn will force the body upwards.
Since Heating will cause expansion of the volume so, on increasing the temperature, the volume of the liquid will increase, and from the formula,
$\Rightarrow {F_B} = {\rho _{liquid}}g{V_{body}}$
We know that
$\Rightarrow {\rho _{liquid}} = \dfrac{M}{V}$
Thus, the relation between buoyant force and volume of the liquid can be given as,
$\Rightarrow {F_B} \propto \dfrac{1}{V}$
Which means by increasing the volume, the buoyant force will decrease.
Thus, we can conclude that on increasing the temperature, the volume will increase which will in turn cause a decrease in the force of Buoyancy.
$\therefore $ Option (B) is the correct Option.

Note
Here we should understand that there are two Volumes in the Archimedes Principle. One refers to the volume of the liquid which manifests itself in the formula through density, and the other refers to the volume of the solid. We should always consider the volume the question is talking about.