A particle moves over three quarters of a circle of radius r. What is the magnitude of its displacement?

As given, a particle moves over three quarters of a circle of radius $r$.

The motion of the particle has been shown in the diagram below:

 $AB$ is the displacement,

To find $AB$, let us use Pythagoras theorem in $\vartriangle AOB$

$AB^2=OA^2+OB^2$

Or $AB^2=r^2+r^2$

Or $AB^2=2r^2$

Or $AB=\sqrt{2r^2}$

Or $AB=r\sqrt{2}$

Thus the magnitude of the displacement is $r\sqrt{2}$.

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Updated on: 10-Oct-2022

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