Question

An old man goes for morning walk on a semicircular track of radius 40 m, if he starts form one end of the track and reaches to the other end, the distance covered by the man and displacement will respectively be:
A) 126 m, 80 m.
B) 80 m, 126 m.
C) 80 m, 252 m.
D) 252 m, 80 m.

Answer 1

Hint:The distance is defined as the total path travelled by the body from initial point to the final point. The displacement of a body is defined as the shortest distance travelled by the body between the initial and final points of the travel of the body.

Complete step by step answer:
It is given that a man goes to walk on a semicircular track of radius 40 m and the man starts his journey from one end of the track to the other end of the track and we need to find the value of distance and displacement of the motion of man.

As distance is the total path travelled by the body in its motion. The distance travelled by the body is the perimeter of the circle. Let us calculate the perimeter of the semicircle. The perimeter of the semicircle is given by,
$P = \pi R$
Where P is the perimeter of the semicircle R is the radius of the semicircle.
$ \Rightarrow P = \pi R$
$ \Rightarrow P = \pi \cdot \left( {40} \right)$
$ \Rightarrow P = 125 \cdot 7m$
$ \Rightarrow P \simeq 125 \cdot 7m$
So the distance travelled is $d = 126m$.

Let us calculate the value of displacement of the man. Displacement is the shortest distance travelled by man between initial and final points. As the initial and final points of the man’s journey are the points of the diameter. So the shortest distance would be equal to the diameter of the semicircle. The displacement is equal to 80 m. The distance and displacement of the old man’s journey is 126 m and 80 m respectively.

The correct option for this problem is option A

Note:The perimeter of a circular track is the total length of the circular track. The perimeter of any circle depends on the radius of the circular track. The displacement of anybody will be zero if the initial and final position of the body after motion is the same.