Assertion:The moment of inertia of rigid body depends only on the mass of the body, its shape and size. Reason: Moment of inertia `I = MR^2` where `M` is the mass of the body and `R` is the radius vector.

Options

A. If both assertion and reason are true 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 both assertion and reason are false.

Explanation

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

### Step 1: Analyze the Assertion
The assertion states that "The moment of inertia of a rigid body depends only on the mass of the body, its shape, and size."

- The moment of inertia (I) is a measure of an object's resistance to changes in its rotational motion. It depends not only on the mass and distribution of that mass but also on the axis about which the object is rotating.
- For example, a rod has different moments of inertia depending on whether it is rotating about its end or its center.

**Conclusion for Step 1**: The assertion is **false** because the moment of inertia also depends on the axis of rotation, not just on mass, shape, and size.

### Step 2: Analyze the Reason
The reason states that "Moment of inertia I = MR² where M is the mass of the body and R is the radius vector."

- This formula is a simplified version and applies specifically to point masses or objects rotating about a specific axis. However, it does not capture the complete picture for rigid bodies with distributed mass.
- The moment of inertia for a rigid body is calculated by integrating the mass distribution relative to the axis of rotation, which varies based on the shape and the axis chosen.

**Conclusion for Step 2**: The reason is also **false** because it does not accurately represent the general case for calculating the moment of inertia of rigid bodies.

### Step 3: Determine the Correct Option
Now that we have established that both the assertion and the reason are false, we can conclude that the correct option is:

**Option D**: Both assertion and reason are false.

### Final Answer
The correct answer to the question is **Option D**: Both assertion and reason are false.

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