The balls of iron and aluminium of same diameter are dipped in water. Which of the following is the correct statement?

Options

A. The upthrust on iron ball will be more than on the aluminium ball.
B. The upthrust on aluminium ball will be more than on the iron ball.
C. The upthrust on both will be the same.
D. None of the above.

Answer

To solve the problem of comparing the upthrust (or buoyant force) on an iron ball and an aluminum ball of the same diameter when dipped in water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Upthrust**:
Upthrust (buoyant force) is the upward force exerted by a fluid on an object submerged in it. According to Archimedes’ principle, the upthrust on an object is equal to the weight of the fluid displaced by the object.

2. **Identify the Given Information**:
We have two balls: one made of iron and the other made of aluminum. Both balls have the same diameter.

3. **Determine the Volume of the Balls**:
Since both balls have the same diameter, they will also have the same radius. The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Because the radius \( r \) is the same for both balls, their volumes will also be the same.

4. **Calculate the Weight of the Water Displaced**:
The weight of the water displaced by each ball will depend on the volume of the ball and the density of water. Since both balls displace the same volume of water, the weight of the water displaced will be the same for both balls.

5. **Apply Archimedes’ Principle**:
Since the upthrust is equal to the weight of the fluid displaced, and both balls displace the same volume of water, the upthrust on both the iron ball and the aluminum ball will be equal.

6. **Conclusion**:
Therefore, the correct statement is that the upthrust on both balls will be the same.

### Final Answer:
The upthrust on both the iron ball and the aluminum ball will be the same.