Correct Option
The correct option is (c) 1 and 3 only.
Explanation
Motion along a closed track requires the object to change direction to maintain the path. The frequency of these changes depends on the geometry of the track. A circle is mathematically viewed as the limiting case of a regular polygon as the number of sides approaches infinity.
Statement-wise Analysis
- Statement 1 is Correct: As the number of sides of a regular polygon increases (e.g., from a square to a hexagon, to an octagon), the shape increasingly resembles a circle. In the limit where the number of sides becomes infinite, the polygon becomes a circle.
- Statement 2 is Incorrect: A rectangular track consists of four straight sides and four corners. An athlete running one complete round must turn at each of the four corners. Therefore, the direction changes four times, not six.
- Statement 3 is Correct: On a circular track, the direction of motion is tangential to the circle at any specific position. Since the tangent changes its orientation continuously along the curve, the direction of motion changes at every point.
Key Takeaway: In polygonal paths, direction changes are discrete (occurring only at corners), whereas in circular motion, the change in direction is continuous at every point.