Flag Mechanics> A particle moving in a circular path of r...
question mark

A particle moving in a circular path of radius Rin such a way that at any instant tangential and radial acceleration are equal. If at t=0 the speed of particle is v find time period to complete first revolution.

sayak maji , 8 Years ago
Grade 11
anser 1 Answers
Manas Shukla

Last Activity: 8 Years ago

Lets assume initial velocity of particle to be = {v_{0}} , so as not to be confused with variable velocity...
Its given a_{t} = v^{2}/ R
Now \frac{\partial v}{\partial t} = \frac{v^{2}}{R}
Integrating we get -\frac{1}{v} = \frac{t}{r} + C
substituting values at t = 0 we find C = -\frac{1}{v_{0}}
Now we know v =\partial x/\partial t
And we know for 1 revolution dx will vary from 0 to 2\Pi R
\frac{\partial x}{\partial t} = \frac{Rv_{0}}{R-v_{0}t}
\int_{0}^{2\Pi R} \partial x = \int_{0}^{t} \frac{Rv_{0}}{R-v_{0}t} \partial t
Solving we get
2\Pi R = \frac{R v_{0}}{-v_{0}} ln (R-v_{0}t)
Cancelling common terms
e^{-2\Pi } = R - v_{0}t
t= \frac{R-e^{-2\Pi }}{v_{0}}
Ask if you have any problems , Best of luck

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...