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Mechanics

Blazing goIITian

Joined:	31 Jan 2007
Post:	1069

21 Sep 2007 00:00:01 IST

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399

find displacement

None

A particle is moving in a circular path of radius r with a uniform speed u

What iis displacement of particle after it has described an angle of 60 degrees

Ans r

please give me a detailed simplified solution

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Comments (5)

ramyani chakrabarty

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Joined: 22 Apr 2007

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21 Sep 2007 00:51:41 IST

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This is to be done geometrically.
consider the particle at the extreme right of the diameter. Then , let the particle travels (1 / 6 ) times the periphery which is 60 degree. Join the initial and final position . This is an equilateral triangle . So the straight line distance from initial to final position i, e, displacement is radius r .

Rakesh OFFLINE

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21 Sep 2007 09:16:06 IST

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i did it by triangle law & i am getting

3 r

and not r

please explain

ankur goyal

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Joined: 17 Apr 2007

Posts: 13

21 Sep 2007 09:34:48 IST

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let x be the displacement
acc to triangle law
x2 = r2 +r2 + 2r.r.cos120
x2 = r2
x = r

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

21 Sep 2007 14:07:41 IST

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Draw a clear figure of the situation.

Complete the triangle by joining centre, initial point and final point.

They will form an equilateral triangle.

So the displacement is the segment which subtends an angle of 60 whose lebgth will bw equal to radius = r.

sumit subhajyoti

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Joined: 2 Aug 2007

Posts: 33

21 Sep 2007 14:22:08 IST

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This can be easily solved by using simple concepts on circle.

let the displacement travelled by the particle from A to B be AB and the centre of the circle be o. so,

<AOB=60degr (given)

since OA=OB(equal radii),

So, <OAB=<OBA=xdegr.

now, in triangle OAB,

2x+60=180

=>x=60degr

since triangle AOB is equilateral,

So, OA=OB=AB=r (solved)

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