Question

Four girls skating on circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in the figure. For which girl displacement is equal to the actual length of the path?

Answer 1

Displacement is the shortest distance between the initial and the final position of the object irrespective of the path traversed by the object for moving from initial position to the final position. The displacement of the object can be zero even though it has covered a distance.

Complete step by step answer:
In this question, it is said that the four girls are skating on the circular ice ground of radius 200m hence the diameter of the ground will be 400m.
All the girls start from a point and finish at point Q diametrically opposite to P
Now we will see all the girls one by one
Girl A:
A start from P and have a semi curve semi-straight motion towards Q and finally ends at Q it is evident here that the distance travelled by A is slightly more than the diameter of the circle because of the curve she moved but as we know the displacement is the shortest distance between final and initial point so her displacement will be 400m only though the distance covered by her will be more than 400 m
Girl B:
The path traversed by B from P to Q is slightly straighter than A but here still some curve movement can be seen so total distance covered will be more than m but the displacement here is still the shortest distance between P and Q I.e.,400m
Girl C:
C moves in a straight line from PO to Q hence her distance travelled will be equal to displacement because the shortest distance between two points can only be given by a straight line
Therefore, Girl C has the same value for distance as well as displacement.

Note:
- The distance travelled cannot be zero.
- Displacement can be zero if the final and initial position coincides like in a circular track if the starting point and endpoint are the same.
- Distance is a scalar quantity whereas the displacement is a vector quantity.