Question

particle is moving in a circular path of radius r find magnitude of displacement of particle after covering 3/4th of circle

Answer 1

displacement : displacement is the minimum path covered by particle or it is the difference of final position to initial position.

Let particle starts to move from A, after completing 3/4th part of circle particle stops at point B.

so, displacement of particle = length of AB [ as shown in figure ]

if we assume O is the centre of circle,

then, ∆AOB is isosceles right angled triangle.

length of AB = hypotenuse

radius of circle = base = height

from Pythagoras theorem,

so, length of AB² = r² + r² = 2r²

or, length of AB = √2r

hence, displacement of particle is √2r