Question

A block of iron is kept at the bottom of a bucket full of water at ${{2}^{o}}C$. The water exerts a buoyant force on the block. If the temperature of the water is increased by ${{1}^{o}}C$ the temperature of the iron block increases by ${{1}^{o}}C$. The buoyant force on the block by the water
a)will increase
b)will decrease
c)will not change
d)may decrease or increase depending on their values of coefficient of expansion

Answer 1

Hint: In the question we are asked to basically determine whether the buoyant force due to the water on the block changes, when the temperature of the water is increased by ${{1}^{o}}C$. To answer this we will first see how the buoyant force changes i.e. on what parameters does it depend on and accordingly determine whether the change in temperature increases the buoyant force.

Formula used: ${{F}_{B}}=\rho gV$

Complete step by step answer:
In the above question it is given to us that the iron block is completely submerged in water. Let us say the Volume of the iron block in water is V. If the density of the water is equal to $\rho $and the acceleration due to gravity is g, than the buoyant force (${{F}_{B}}$) on the iron block is given by,
${{F}_{B}}=\rho gV$
It is to be noted that the density of water changes with temperature. The density of water keeps on increasing until it attains a maximum value of $1000kg{{m}^{-3}}$at ${{4}^{o}}C$. It is given in the question that the temperature of the water increases from ${{1}^{o}}C$ to ${{3}^{o}}C$. During this change the density of the water basically increases. Since the buoyant force is directly proportional to the density of water, the buoyant force on the iron block will therefore increase.

So, the correct answer is “Option A”.

Note: It is to be noted that if we keep on increasing the temperature of water after ${{4}^{o}}C$ the density of water will again slowly decrease. Hence the buoyant force on the block due to water after ${{4}^{o}}C$ will successively keep on decreasing. From this we can also conclude that the buoyant force will be maximum at ${{4}^{o}}C$.