Question

An aluminum sphere is dipped into water at $10{}^{\circ }C$. 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 $r$ of sphere

Answer 1

When a body is dipped inside any fluid, the body feels lighter, although the mass and the acceleration due to gravity acting on it remains constant. It feels lighter because the fluid tends to push it upwards towards the surface naturally. This upward push is known as buoyant force or buoyancy.

Complete step by step solution:
Hence, the buoyant force is the force that helps objects to float. The word ‘buoy’ means to float in the Dutch language.
Buoyancy or Buoyant force = weight of liquid displaced
Pressure increases with depth $(\because P=\rho gh)$. As we go deeper into a liquid, the pressure increases, which increases the force acting on the submerged body.
On changing the water temperature, heat is also given to the aluminum sphere, which in return expands uniformly as per its coefficient of volumetric expansion, increasing the volume of the sphere.
Since the mass remains constant therefore the density of the sphere decreases as volume increases $\because density=\dfrac{mass}{Volume}$
$\Rightarrow \rho =\dfrac{m}{V}$
$\therefore m=\rho V$
weight of liquid displaced = weight of body submerged in liquid
$\Rightarrow mg$
$\Rightarrow (\rho V)g$
Now, as the volume increases, the density decreases, neutralizing the change caused by each other.
Therefore, the buoyant force remains constant.

The correct answer is [C], will remain constant.

Note: Liquid displaced is the amount of liquid in whose space the new object has taken inside the container or the water body. Either it flows out of the container, or if there is enough space in the container, then the liquid level rises. Also, even if we consider that the density of water has decreased, in that case, the volume of the water displaced is increased, hence neutralizing the overall effect.