A block of iron is kept at the bottom of a bucket full of water at `2^@C`. The water exerts bouyant force on the block. If the temperature of water is increased by `1^@C` the temperature of iron block also increases by `1^@C`. The bouyant force on the block by water

Options

A. will increases
B. will decreases
C. will not change
D. may decreases or increases depending on the values of their coefficient of expansion

Explanation

To find the buoyant force exerted on a block of iron by water when the temperature of the water is increased, we can follow these steps:

### Step 1: Understand the concept of buoyant force
The buoyant force (Fb) acting on an object submerged in a fluid is given by Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. Mathematically, it can be expressed as:
\[ F_b = \rho \cdot g \cdot V \]
where:
- \( F_b \) = buoyant force
- \( \rho \) = density of the fluid (water in this case)
- \( g \) = acceleration due to gravity
- \( V \) = volume of the fluid displaced (which is equal to the volume of the submerged part of the object)

### Step 2: Analyze the effect of temperature on water density
Initially, the water is at 2°C. As the temperature of the water increases by 1°C, the new temperature becomes 3°C. Water has its maximum density at 4°C, which means that as the temperature increases from 2°C to 3°C, the density of water will increase.

### Step 3: Consider the volume of the block
The volume of water displaced by the block is equal to the volume of the block itself. As the temperature of the iron block increases by 1°C, it may expand slightly, but for most practical purposes, the volume change of the iron block is negligible compared to the change in water density.

### Step 4: Calculate the buoyant force
Since the density of water increases as the temperature rises from 2°C to 3°C, the buoyant force will also increase. The buoyant force can be expressed as:
\[ F_b = \rho_{new} \cdot g \cdot V \]
where \( \rho_{new} \) is the density of water at 3°C.

### Step 5: Conclusion
Thus, the buoyant force on the block of iron by water will increase as the temperature of the water increases from 2°C to 3°C due to the increase in density of the water.