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A particle moving in a circular path of radius R in 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.
A particle moving in a circular path of radius R  in 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.


4 years ago

Manas Shukla
102 Points
							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

4 years ago
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### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions