A boy of mass $ 40 \mathrm{~kg} $ moves on a circular track of radius $ 21 \mathrm{~m} $. Find displacement and distance when initial and final position are diametrically opposite points.

Given:

Radius of the circular track, $r$ = 21 m

To find: Displacement & Distance.

Solution:

As the initial and final positions are diametrically opposite points. It means the boy completes half-round (semicircle or half-circle).

To find the distance, we need to find the circumference of the semicircle (half-circle).

We know that-

$Circumference,\ (C)=2\pi {r}$

Thus circumference of the semicircle (half circle) $=\frac {2\pi {r}}{2}=\pi {r}$

Hence, 

Distance when boy completes half-round $=\frac {22}{7}\times {21}=22\times {3}=66m$

Displacement = shortest distance between initial position and the final position = diameter of the circle $=2\times {r}=2\times {21}=42m$

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Updated on: 10-Oct-2022

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