Assertion: When a sphere of perfectly hard material is rolled on a perfectly hard surface then sphere never stops.
Reason: Friction becomes zero at the contact

Options

A. If both assertion and reason are correct and reason is the correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct.

Explanation

To solve the question regarding the assertion and reason, we will analyze both statements step by step.

### Step 1: Understanding the Assertion
The assertion states: "When a sphere of perfectly hard material is rolled on a perfectly hard surface then the sphere never stops."

- **Analysis**: In an ideal scenario where both the sphere and the surface are perfectly hard, there is no deformation of either object when they come into contact. This means that the sphere can roll indefinitely without losing energy due to deformation.

### Step 2: Understanding the Reason
The reason states: "Friction becomes zero at the contact."

- **Analysis**: For a rolling object, static friction is what allows it to roll without slipping. If the sphere rolls without slipping, the condition \( v = r \omega \) holds true, where \( v \) is the linear velocity, \( r \) is the radius, and \( \omega \) is the angular velocity. In this case, there is no relative motion at the point of contact, which implies that the frictional force is zero.

### Step 3: Evaluating the Truth of Both Statements
- Both the assertion and the reason are true in the context of perfectly hard materials and surfaces. The assertion is correct because the sphere will not stop rolling if there is no energy loss due to friction or deformation. The reason is also correct because, under these ideal conditions, there is no relative motion at the contact point, leading to zero friction.

### Step 4: Conclusion
Since both statements are true and the reason correctly explains the assertion, we conclude that:

- **Final Answer**: Both the assertion and reason are true, and the reason is the correct explanation of the assertion.