A sphere of iron and another of wood the same radius are held under water. Compare the upthrust on the two spheres.

Answer

To solve the problem of comparing the upthrust (buoyant force) on an iron sphere and a wooden sphere of the same radius when submerged in water, we can follow these steps:

### Step 1: Understand the concept of upthrust
Upthrust, or 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.

### Step 2: Determine the volume of the spheres
Since both spheres (iron and wood) have the same radius, we can calculate their volumes using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the spheres.

### Step 3: Compare the volumes
Since both spheres have the same radius, their volumes will be equal:
\[ V_{\text{iron}} = V_{\text{wood}} \]

### Step 4: Calculate the weight of the water displaced
The weight of the water displaced by each sphere can be calculated using the formula:
\[ \text{Weight of displaced water} = \text{Volume of sphere} \times \text{Density of water} \times g \]
where \( g \) is the acceleration due to gravity.

Since both spheres displace the same volume of water, the weight of the water displaced by both spheres will also be the same.

### Step 5: Conclude the comparison of upthrust
Since the upthrust (buoyant force) is equal to the weight of the fluid displaced, and both spheres displace the same volume of water, the upthrust on both the iron sphere and the wooden sphere will be equal.

### Final Conclusion
The upthrust on the iron sphere and the wooden sphere is the same.

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