A body travels a distance of pi meter over a semicircle of radius r. what is
the displacement of the particles
Answers
Given : A body travels a distance of πr meter over a semicircle of radius r.
To Find : the displacement of the particles
Solution:
Circumference of circle = 2πr
Circumference of semi circle = πr
A body travels a distance of πr meter over a semicircle of radius r.
Hence body just reached opposite point
Hence Displacement = Diameter
Diameter = 2 * radius = 2r
=> displacement of the particle = 2r
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Answer:
Step-by-step explanation:
If a body travels a distance of π meters along a semicircle of radius r, the displacement of the particle can be calculated using the concept of vectors. The displacement is the straight-line distance between the initial and final positions of the body.
In this case, the initial and final positions are the endpoints of the semicircle's diameter. Let's assume the initial position is at the origin (0,0) and the final position is at (r,0) on the x-axis.
The displacement vector, represented as Δx, can be calculated using the Pythagorean theorem:
Δx = √[(r - 0)^2 + (0 - 0)^2]
= √(r^2 + 0^2)
= √(r^2)
= r
Therefore, the displacement of the particle is equal to the radius of the semicircle, r.