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Motion In A Plane

Question
CBSEENPH11018443

Three girls skating on a circular ice ground of radius 200 m start from point P on the edge of the ground and reach a point Q diametrically opposite to P following different path as shown. What is the magnitude of displacement vector for each? For which girl is this equal to the actual length of path skate? 

                      

Solution
Given, 
Radius of the skating ground = 200 m 
The initial and final position of all grls are same. Hence, displacement of each girl is same. 
∴    Displacement equals PQ with rightwards arrow on top 
Magnitude of displacemnt is given by,
open vertical bar Displacement close vertical bar space equals space 2 space left parenthesis radius space of space track right parenthesis space equals space 400 straight m 
From the figure, girl B skates along the straight path PQ. Therefore, for girl B, the magnitude of displacement and distance will be equal.