Question:
A body moves on three quarters of circle of radius r .find the values of the displacement and distance travelled by the body
Answer:
A quarter of a circle is 90∘90∘, and three quarters of a circle is 3×90∘=270∘3×90∘=270∘.
- Displacement: Displacement is the straight-line distance between the initial and final positions of the body. Since the body is moving along three-quarters of a circle, it starts and ends at the same point, but the direction changes.
For three-quarters of a circle, the displacement will be the diameter of the circle. The diameter is twice the radius (2r).
Therefore, the displacement is 2r.
- Distance Traveled: Distance traveled is the total path length covered by the body during its motion.
For three-quarters of a circle, the distance traveled will be the length of three-quarters of the circumference of the circle.
Circumference of the circle = 2πr
Distance traveled = 3/4×2πr =3πr/2
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