A particle is moving in a circle of radius R with constant speed . The time period of particle is T=1 Second in a time t = T/6 , If the difference between average speed and magnitude of average velocity of the partical is 2m/sec, find the radius of the circle(in meteres)

Dear Student,

Please find below the solution to the asked query:

Given that the time period of the particle is T. Then, the angular velocity is,

ω=2πT radsec
So, in time t = T/6, the particle will be having the angular displacement,

θ=ωt=2πT×T6=π3
Therefore, the distance travelled by the body is,

distance =π32π×2πRdistance=πR3

Displacement of the body is,

dispacement=R

So, the magnitude of velocity is,

V=Displacementtime=RT6=6RT

The magnitude of speed is,

S=Distancetime=πR3T6=2πRT

Therefore, the difference of the magnitude of the speed and the magnitude of the velocity is,

Difference = 2πRT-6RT2π-6RT=2R=22π-6R=20.28=507R=7.14 m


 

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