Question

A particle is moving along a circle of radius 4 metre find the distance travelled by it and magnitude of displacement if it traverse an angle of 150 degree?​

Answer 1

Answer:

distance  = 10.472 m

displacement = 7.727 m

Explanation:

given:

radius = 4 m

θ = 150 °

distance = ?

displacement = ?

distance = 2πrθ / 360°

               = 2πr 150° /360°

distance  = 10.472 m

let the starting point be 'a' vector and final point be 'b' vector . Each vector will have equal magnitude which is equal to radius of the circle.

Now ,displacement is the difference between the two vectors.

we know that,

when magnitude of two vectors are equal then,

difference of the vectors = 2r sinθ/2

where,

r = magnitude of one vector  = radius of the circle

putting the values,

displacement = 2 * 4 * sin (150/2)

                      = 8 * sin(75)

                     = 8 * sin( 45 + 30)

                      = 8* [ sin 45 cos 30 + cos 45 sin 30]

                        = 8 * [($\frac{1}{\sqrt2}$)($\frac{\sqrt3}{2}$) +  ($\frac{1}{\sqrt2}$)($\frac{1}{2}$)]

                      = 8 * [$\frac{\sqrt3 + 1}{2\sqrt2}$]

                      = ($2\sqrt{2}$)($\sqrt{3} + 1$)

on simplification

displacement = 7.727 m

Hope it helps !