Question

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

Answer 1

displacement is the shortest path between source and destination.

Hence if we join the point A and B we get a Right angled triangle.

where

(displacement)=Hypotenuse

 and other two sides of triangle with sides r.

Displacement =√(r² +r²)

=√(2r²)

=r*√(2)

=1.41*r meters

∴ Displacement covered by particle is 1.414*r m

Answer 2

Given,

A particle covers three quarters of a circle of radius R.

Distance travelled = 3/4

(circumference of circle)

=3/4 ( 2 x pie x r)

= 3/2 ( pie x r).

Displacement = Shortest path

= IF WE JOIN POINT A and B we get right angle triangle with Hypotenuse (displacement) and other two sides of triangle with sides r.

Displacement =Sqr(r^2 +r^2)

=sqr(2r^2)

=r x sqr(2)

=1.41 x r meters

∴ Displacement covered by particle is 1.414 x r m