Question

A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2min20 sec. the ratio of displacement/distance ts

Answer 1

Answer:

Firstly the Circumference of the track = 2(Pi) R or (Pi) D

r is radius and d is diameter

So he covers that distance in 40 seconds, his speed = distance/time = (Pi)D/40

So, in 2 minute 20 seconds, i.e = 140 seconds, Distance = Speed * Time

= (Pi)D/40*140 = 3.5 (Pi)D

However, displacement, being the shortest distance between starting and ending points, that’s a different ball park altogether.

Now, we know (Pi)D is the circumference,

From this we know he did, 3.5 Laps ( 3.5(Pi)D/(Pi) D)

That means, he is exactly on the opposite side of where he started, which doesn’t exist on a circle, because circle doesn’t have sides :P

What I mean to say is that, he covered half of the circumference, and hence, he is on the point on the circle, that is the farthest point than any other point on the circle.

If a diameter is drawn from where he started, his stopping point is exactly on the other point of the diameter, and hence displacement is D

And the ratio of Distance : Displacement is hence 3.5(Pi) D/D = 3.5(Pi):1

or 11:1 (Pi is taken as 22/7)

And Displacement to Distance is 1:11

Hope it helps