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As shown in Fig. 1.26, a child starting his journey from point $O$ reaches to $A$ first, then travels one-quarter of a circle along $AB$ and finally returns to $O .$ If radius of the circle be $r,$ then find the total displacement of the child.

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\frac{25}{7} r

1 m

0

\frac{25}{5} r

answer is C.

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Detailed Solution

The total displacement of the child is zero.
The displacement is defined as the shortest distance between two points.
Taking the radius of the circle

r

,
and the circumference of the circle,

2 πr,

because it covers

1 / 4

of the circumference of the circle,
The distance travelled will be equal to

πr / 2

along AB.
The total distance is now

OA + AB + BO .

OA = BO = r

\frac{π r}{2} + r + r = 2 r + \frac{πr}{2}

= \frac{(4 πr + r) 1}{2}

As the child starts his journey from point

O

reaches

A

first, then travels one-quarter of a circle along

AB

, and finally returns to point

O

. As the child comes to the point from where he begins his journey.

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