A body covers a distance 1metre along a semicircular path.calculate the magnitude of the body and the ratio of distance to displacement
distance=1m
displacement= 2/PI
ratio: (2/PI)/1=2/PI
To calculate the magnitude of the body, we need to know the radius of the semicircular path. Let's assume the radius of the path is 'r' meters.
1. Magnitude of the Body:
The magnitude of the body can be calculated using the formula for the circumference of a circle:
Circumference = 2πr
Since we have a semicircle, we need to divide the circumference by 2:
Semicircular distance = 1 meter
Circumference/2 = 1 meter
Therefore,
2πr/2 = 1 meter
Simplifying,
πr = 1 meter
r = 1/π meters
Thus, the radius of the semicircular path is 1/π meters. Therefore, the magnitude of the body is equal to the circumference of the semicircle.
2. Ratio of Distance to Displacement:
The distance covered by the body is equal to the circumference of the semicircular path, which we have determined as 2πr.
The displacement is the straight-line distance between the initial and final positions of the body. For a semicircular path, the displacement is equal to the diameter of the circle, which is 2r.
Therefore, the ratio of distance to displacement is:
Ratio of distance to displacement = (2πr) / (2r)
The '2r' terms cancel out, simplifying the ratio to:
Ratio of distance to displacement = π
So, the ratio of distance to displacement for this semicircular path is equal to π (approximately 3.14159).