Assertion : A solid sphere and a hollow sphere both of same material are immersed in a liquid , then change in weight in both the spheres will be same.
Reason : Upthrust depends upon the volume of the solid immersed not the mass.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that a solid sphere and a hollow sphere made of the same material, when immersed in a liquid, will experience the same change in weight.

### Step 2: Analyze the Reason
The reason given is that upthrust (or buoyant force) depends on the volume of the solid immersed in the liquid, not on the mass of the object.

### Step 3: Apply Archimedes' Principle
According to Archimedes' principle, the buoyant force (upthrust) acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This means:
\[ F_{\text{upthrust}} = V \cdot \rho_L \cdot g \]
where:
- \( V \) = volume of the object submerged
- \( \rho_L \) = density of the liquid
- \( g \) = acceleration due to gravity

### Step 4: Compare the Volumes
Since both the solid sphere and the hollow sphere are made of the same material and are of the same size, they will displace the same volume of liquid when fully immersed. Thus, the volume \( V \) in the equation for buoyant force will be the same for both spheres.

### Step 5: Calculate Change in Weight
The change in weight of each sphere when immersed in the liquid can be expressed as:
\[ \Delta W = W - F_{\text{upthrust}} \]
where \( W \) is the weight of the sphere in air.

Since the upthrust is the same for both spheres (as established above), the change in weight \( \Delta W \) will also be the same for both spheres.

### Step 6: Conclusion
Both the assertion and the reason are correct. The assertion is true because the change in weight for both spheres is the same due to equal upthrust, and the reason is also true because upthrust depends on the volume of the object, not its mass.

### Final Answer
Both the assertion and the reason are correct, and the reason is the correct explanation for the assertion.

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