A body moves along the circumference of a circular track of radius R. What is the displacement of the body when it covers 3/4 the of its circumference -

CONCEPT:

Displacement is the distance between the initial and final position after the motion or journey of an object.

• Displacement is a vector quantity and can be obtained from the difference of position coordinates of the initial and final positions.

CALCULATION:

Let us assume that the body starts the journey from point Q and reaches point T after completing 3/4 of the circumference.

Now, the initial point is P and the final point is T. Hence, displacement is equal to the distance QT.

From the figure,

OT = R; OQ = R

Therefore,  

\(\Rightarrow QT=\sqrt{OQ^2 + OT^2} = \sqrt{R^2 + R^2} = \sqrt{2R^2}=R\sqrt{2}\)