Displacement of a person moving from X to Y along a semicircular path of radius r is 200 m. What is the distance travelled by him ?

Options

A. `314 m`
B. `200 m`
C. `214 m`
D. `100 m`

Answer

A

Explanation

Give, displacement = 200 m
Distance travelled by the person from X to Y is equal to the circumference of the semicircular path
`therefore x = 2pi D rArr (therefore "Diameter" = ("Radius")/(2))` ….(i)
According to the question, the shortest distance between the final position Y and initial position X is XY = 2r.

`therefore` The displacement traversed by the person is 2r.
`therefore 200 = 2r rArr r =100m`
Putting r = 100m in Eq. (i), we get
Distance `x=pi xx 100 rArr x=314 m`