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A particle move along a circular arc of radius R making an angle of θ at center. The magnitude of displacement is: 1) 2Rsinθ/2. 2) 2Rsinθ. 3) Rsinθ/2. 4) Rsinθ? Correct option is A can you explain how?
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A particle move along a circular arc of radius R making an angle of θ ...
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A particle move along a circular arc of radius R making an angle of θ ...
Explanation:

  • Displacement: The displacement is the shortest distance between the initial and final positions of the particle. In circular motion, the displacement is represented by a straight line drawn from the initial position to the final position, passing through the center of the circle.

  • Formula: The magnitude of displacement can be calculated using the formula: Displacement = 2Rsin(θ/2) where R is the radius of the circle and θ is the angle made by the particle at the center of the circle.

  • Explanation of formula: The formula is derived as follows:

    • Consider a circular arc of radius R, making an angle θ at the center.

    • Draw a line perpendicular to the chord passing through the center of the circle.

    • The length of this perpendicular line is Rsin(θ/2).

    • Since the displacement is the shortest distance between the initial and final positions, the magnitude of displacement is equal to twice the length of this perpendicular line.

    • Therefore, Displacement = 2Rsin(θ/2).



  • Answer: Using the formula, Displacement = 2Rsin(θ/2) = 2Rsin(θ/2) = Rsinθ.

  • Correct option: Option A, i.e., 2Rsinθ/2, is the correct option.

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A particle move along a circular arc of radius R making an angle of θ at center. The magnitude of displacement is: 1) 2Rsinθ/2. 2) 2Rsinθ. 3) Rsinθ/2. 4) Rsinθ? Correct option is A can you explain how?
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