A disc is rolling on an inclined plane without slipping. The velocity of centre of mass is `V`. These other point on the disc lie on a circular are having same speed as centre of mass.
When a disc is rolling on an inclined plane. The magnitude of velocities of all the point from the contact point is same, having distance equal to radius `r`.

Options

A. Statement I is True, Statement II is True, Statement ll is a correct explanation for Statement I.
B. Statement I is True, Statement II is True, Statement II is NOT a correct explanation for Statement I
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Explanation

To solve the problem of a disc rolling on an inclined plane without slipping, we can break it down into the following steps:

### Step 1: Understand the Motion of the Disc
When a disc rolls without slipping, the point of contact with the inclined plane has a velocity of zero. This is because it is momentarily at rest relative to the surface it is in contact with.

**Hint:** Remember that in rolling motion, the point of contact does not move relative to the surface.

### Step 2: Identify the Velocity of the Centre of Mass
Let the velocity of the centre of mass of the disc be denoted as \( V \). This is the linear velocity of the disc as it rolls down the incline.

**Hint:** The centre of mass is the average position of all the mass in the disc, and it moves with velocity \( V \).

### Step 3: Relate the Linear Velocity to Angular Velocity
For a disc rolling without slipping, the relationship between the linear velocity \( V \) of the centre of mass and the angular velocity \( \omega \) is given by:
\[ V = r \cdot \omega \]
where \( r \) is the radius of the disc.

**Hint:** This relationship is crucial in rolling motion; it connects linear and angular velocities.

### Step 4: Analyze Other Points on the Disc
Consider a point \( P \) on the disc that is a distance \( r \) from the point of contact \( A \). The velocity of point \( P \) can be expressed as:
\[ V_P = r \cdot \omega \]
Since the disc is rolling without slipping, the velocity of point \( P \) will also be equal to \( V \).

**Hint:** All points on the disc that are at a distance \( r \) from the point of contact will have the same speed as the centre of mass.

### Step 5: Conclusion
Since all points on the disc that are a distance \( r \) from the contact point have the same speed as the centre of mass, we can conclude that the statement in the question is true.

**Hint:** This conclusion reinforces the concept of rolling without slipping, where the velocities of points on the rolling object are consistent with the motion of the centre of mass.

### Final Answer
The statement is true: the magnitude of velocities of all points from the contact point is the same, having a distance equal to the radius \( r \).