Assertion : A solid sphere and a hollow sphere of same material and same radius are kept at same temperature in atmosphere. Rate of cooling of hollow sphere will be more.
Reason : If all other conditions are same, then rate of cooling is inversely proportional to the mass of body.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the 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 of the same material and radius, when kept at the same temperature, will have a greater rate of cooling for the hollow sphere.

### Step 2: Understand the Reason
The reason states that the rate of cooling is inversely proportional to the mass of the body, given that all other conditions remain the same.

### Step 3: Analyze the Mass of the Spheres
1. **Solid Sphere**: The mass of a solid sphere can be calculated using the formula for the volume of a sphere \( V = \frac{4}{3} \pi r^3 \) and the density \( \rho \):
\[ m_{\text{solid}} = \rho \cdot V = \rho \cdot \frac{4}{3} \pi r^3 \]

2. **Hollow Sphere**: A hollow sphere has less mass because it has a cavity inside. The mass can be calculated similarly, but it will be less than that of the solid sphere for the same outer radius.

### Step 4: Apply Newton's Law of Cooling
According to Newton's Law of Cooling, the rate of heat loss (cooling) is proportional to the surface area and inversely proportional to the mass of the object:
\[ \text{Rate of cooling} \propto \frac{A}{m} \]
Where \( A \) is the surface area and \( m \) is the mass.

### Step 5: Compare the Cooling Rates
Since the hollow sphere has less mass than the solid sphere (due to its hollow nature), the rate of cooling for the hollow sphere will be higher because:
\[ \text{Rate of cooling}_{\text{hollow}} > \text{Rate of cooling}_{\text{solid}} \]

### Step 6: Conclusion
Both the assertion and the reason are true. The reason correctly explains why the hollow sphere cools faster than the solid sphere.

### Final Answer
- Assertion: True
- Reason: True
- Explanation: The reason is the correct explanation for the assertion.