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Q.


A particle moves in a circle of radius R. In half the period of revolution, the displacement will be and distance covered is ____of the circumference of the circle.


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Detailed Solution

Concept- The distance between two points is determined by displacement, which is the shortest distance. Depending on the direction, displacement can be either positive or negative. But the concept of distance is usually good. Always, the distance will be greater than or equal to the displacement.
The displacement is the shortest distance between the starting point and the destination, whereas distance is the actual path travelled by the body and is a scalar variable. Dimension and direction are attributes of displacement. No distance may be zero or negative.
If a particle follows a circular route of radius R, the semicircle is implied by half of the revolution.
Question ImageTherefore, the particle will travel a distance equal to half of the circle's circumference.
a circle's radius R's circumference,
 Question Image                The distance covered by the particle will be,    Question Image         Since the particle made one half of a rotation, its displacement will equal the circle's diameter. The particle will move in a clockwise manner in this diagram. The most displacement a body may make in a circular motion is measured by its diameter. The particle will therefore be at the exact opposite position from its starting point. Depending on the reference point we are thinking about, the direction will change.
Question Image, where the vector sign implies the direction of displacement.
Additional details:
Two types of uniform circular motion are possible. Depending on the speed, circular motion can be either uniform or non-uniform.
An item moving in a circular direction while maintaining a constant speed is said to be in uniform circular motion. The duration is how long it takes for one revolution to finish.Question Image, where v is the velocity of rotation.     A uniform circular motion will have a constant speed but a variable direction at each point on the circle. The frequency of a particle is how many revolutions it completes in one unit of time. The velocity is always tangent to the object's path in a uniform circular motion. The motion is specified by this tangent.                                                 Hence, the answer is half.
 
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A particle moves in a circle of radius R. In half the period of revolution, the displacement will be and distance covered is ____of the circumference of the circle.