A small ball of mass 1 kg is inside a circle of radius 2 m at one end of the diameter. If the small ball covers quarter circle the displacement of the circle of radius 2m will be ? Mass of large circle is 10 kg?

To determine the displacement of the small ball after it covers a quarter of the circle, we first need to clarify what we mean by "displacement." Displacement refers to the shortest distance from the initial position to the final position, regardless of the path taken. In this case, the ball starts at one end of the diameter of the circle and moves along the arc of the circle.

Understanding the Movement

The small ball begins at one end of the diameter of the circle, which we can label as point A. After covering a quarter of the circle, it will arrive at point B, which is directly perpendicular to point A, at the top of the circle.

Visualizing the Circle

Imagine the circle with a radius of 2 meters. The diameter runs horizontally, and the ball starts at the leftmost point (point A). After moving a quarter of the way around the circle, it reaches the topmost point (point B). The coordinates of these points can be represented as follows:

• Point A (initial position): (-2, 0)
• Point B (final position): (0, 2)

Calculating Displacement

To find the displacement, we can use the distance formula between the two points. The formula for the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

d = √((x_2 - x_1)² + (y_2 - y_1)²)

Substituting the coordinates of points A and B into the formula:

• x₁ = -2, y₁ = 0
• x₂ = 0, y₂ = 2

Now, plug these values into the distance formula:

d = √((0 - (-2))² + (2 - 0)²)

d = √((2)² + (2)²)

d = √(4 + 4)

d = √8

d = 2√2

Final Result

The displacement of the small ball after it covers a quarter of the circle is \(2\sqrt{2}\) meters, which is approximately 2.83 meters. This value represents the straight-line distance from the starting point to the endpoint, illustrating how displacement differs from the actual path traveled along the arc of the circle.

In summary, while the ball travels a distance along the curve of the circle, its displacement is simply the straight-line distance between its initial and final positions. This concept is crucial in physics, as it helps differentiate between the total distance traveled and the net change in position.