Assertion : The field strength at the centre of a ring is zero
Reason : At the centre of the ring, slope of V-r graph is zero.\

Options

A. If both Assertin and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct 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

Answer

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

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that "The field strength at the center of a ring is zero."
- A ring of mass exerts gravitational force on a point located at its center. Due to symmetry, the gravitational forces exerted by all the mass elements of the ring cancel each other out at the center. Therefore, the net gravitational field strength at the center of the ring is indeed zero.

2. **Understanding the Reason**:
The reason states that "At the center of the ring, the slope of the V-r graph is zero."
- In gravitational terms, V represents the gravitational potential, and r represents the distance from the center of the ring. The gravitational field strength (E) is related to the gravitational potential (V) by the equation:
\[ E = -\frac{dV}{dr} \]
- If the gravitational field strength (E) is zero (as established in the assertion), then:
\[ E = 0 \implies -\frac{dV}{dr} = 0 \implies \frac{dV}{dr} = 0 \]
- This means that the slope of the V-r graph, which represents the rate of change of gravitational potential with respect to distance, is indeed zero at the center of the ring.

3. **Conclusion**:
- Since both the assertion and the reason are true, and the reason correctly explains the assertion, we can conclude that both statements are valid.

### Final Answer:
- The assertion is true, and the reason is also true, with the reason correctly explaining the assertion.