Question

An aluminium sphere is dipped into water at $10^\circ {\text{C}}$, 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 $r$of the sphere.

Answer 1

There will be a small change in the aluminium volume as the temperature increases, and this will lead to an increase in volume of sphere. The pressure exerted by the sphere will reduce due to an increase, as well as the volume immersed also will decrease due to the above.

Complete step by step answer:
Temperature-Volume Law: This law defines that the volume of gas kept at constant pressure for a given quantity is directly proportional to temperature of Kelvin. The temperature therefore goes up as the amount goes up, and vice versa.
Therefore, if temperature increases, volume of the sphere also increases.

When the temperature is kept constant, according to Boyle's law, the volume of a given quantity of gas becomes inversely proportional to pressure. Equal quantities among all gases match the number of molecules under the same conditions of temperature or pressure (Avogadro's law).
Therefore, if volume increases the pressure exerted by the sphere decreases.

The rising water's upward force is the buoyant force exerted by fluid on the object; this is so if the object floats and sinks. When the depth of the object increases, so will the pressure of the fluid increase. Therefore, friction boosts the buoyant force, which is proportional to the weight of the scattered water.

Therefore, if the pressure decreases the force of buoyancy also decreases.

So, the correct answer is “Option B”.

Note:
In order to answer this question we must know the relation between temperature and volume, volume and pressure, and pressure and force of buoyancy.

Remember that,
Temperature is directly proportional to volume.
Volume is inversely proportional to pressure.
Pressure is directly proportional to force of buoyancy.