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A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is :
A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is :
Updated On: Nov 24, 2024
- 6 km
- √8 km
- 4 km
- 8 km
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The Correct Option is B
Solution and Explanation
Since the cyclist travels along the circumference from point P to point S, which are opposite ends of the diameter of the circle, we can visualize the displacement as the straight-line distance between P and S.
1. Determine the Displacement:
- The radius R of the circular ground is given as 2 km.
- Points P and S form a diameter of the circle.
- The displacement from P to S is the length of the diagonal of the square formed by the radii OP and OS.
Using the Pythagorean theorem, we find:
\[ \text{Displacement} = R\sqrt{2} = 2\sqrt{2} = \sqrt{8} \, \text{km}. \]
Answer: \(\sqrt{8} \, \text{km}\)
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