Which of the following statements are correct for instantaneous axis of rotation?

Options

A. Acceleration of every point lying on the axis must be equal to zero
B. Velocity of a point distance r from the axis is equal to `romega`
C. if moment of inertia of a body about the axis is `I` and angular velocity is (`omega`), then kinetic energy of the body is equal to `Iomega^(2)//2`
D. Moment of inertia of a body is least about nstantaneous axis of rotation among all the parallel axes.

Explanation

To determine which statements are correct regarding the instantaneous axis of rotation, we will analyze each option step by step.

### Step 1: Understanding the Instantaneous Axis of Rotation
The instantaneous axis of rotation is a line about which a body rotates at a particular instant. For a rolling object, such as a wheel, this axis can be found at a point on the ground directly beneath the center of the wheel.

### Step 2: Analyzing the Options
1. **Option A: Acceleration of every point lying on the axis must be equal to zero.**
- This statement is incorrect. While the instantaneous axis of rotation is a point where the velocity is momentarily zero, the acceleration of points on the axis can be non-zero. For example, the point A (the center of the wheel) can have a vertical acceleration due to the angular motion of the wheel.

2. **Option B: Velocity of a point with a distance r from the axis is equal to rω.**
- This statement is correct. The linear velocity (v) of a point at a distance (r) from the instantaneous axis of rotation is given by the equation v = rω, where ω is the angular velocity.

3. **Option C: If the moment of inertia of a body about the axis is I, then the kinetic energy of the body is equal to (1/2)Iω².**
- This statement is correct. The kinetic energy (KE) associated with the rotation of a body about an axis is given by KE = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity.

4. **Option D: Moment of inertia of a body is least about the instantaneous axis of rotation among all the parallel axes.**
- This statement is incorrect. The moment of inertia about the instantaneous axis of rotation is not necessarily the least compared to all parallel axes. The parallel axis theorem states that the moment of inertia about any axis is equal to the moment of inertia about a parallel axis through the center of mass plus the mass times the square of the distance between the two axes.

### Conclusion
Based on the analysis:
- **Correct Options**: B and C
- **Incorrect Options**: A and D

### Summary of the Correct Statements
- **B**: Velocity of a point with a distance r from the axis is equal to rω.
- **C**: If the moment of inertia of a body about the axis is I, then the kinetic energy of the body is equal to (1/2)Iω².