Statement-1: There are two spheres made of same amount of material, one of them is hollow and other is solid. They are heated to same temperature and left in identical surroundigs. The initial rate of cooling will be greater for hollow sphere. Statement-2: The rate of heat loss depends on surface area and temperature.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Answer

To solve the problem, we need to analyze the two statements provided and understand the principles of heat transfer, particularly in relation to the surface area and temperature of the objects involved.

### Step-by-Step Solution:

1. **Understanding the Statements**:
- **Statement 1**: The hollow sphere will cool down faster than the solid sphere when both are made of the same material and heated to the same temperature.
- **Statement 2**: The rate of heat loss from an object depends on its surface area and the temperature difference between the object and its surroundings.

2. **Analyzing Statement 1**:
- Both spheres are made of the same amount of material, which means they have the same mass.
- The hollow sphere has a larger surface area compared to the solid sphere because it has a cavity inside.
- Since the rate of cooling is influenced by the surface area, a larger surface area will lead to a higher rate of heat loss.

3. **Applying the Concept of Heat Loss**:
- The rate of heat loss (P) can be described by Newton's Law of Cooling, which states that:
\[ P = k \cdot A \cdot (T - T_0) \]
where:
- \( P \) is the power (rate of heat loss),
- \( k \) is a constant,
- \( A \) is the surface area,
- \( T \) is the temperature of the object,
- \( T_0 \) is the surrounding temperature.
- Since both spheres are at the same temperature initially and are in the same surroundings, the difference in cooling rates will primarily depend on their surface areas.

4. **Comparing Surface Areas**:
- The hollow sphere has a greater surface area than the solid sphere, which means it will lose heat at a faster rate.
- Therefore, the initial rate of cooling will indeed be greater for the hollow sphere.

5. **Conclusion**:
- Statement 1 is true because the hollow sphere has a greater surface area leading to a higher rate of cooling.
- Statement 2 is also true as it explains why the hollow sphere cools faster due to its larger surface area.

### Final Answer:
Both statements are true, and Statement 2 provides the correct explanation for Statement 1.

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