NTA Abhyas JEE Main2020PhysicsLaws of MotionPractice
A particle is moving in a circle of radius R in such a way that at any instant the tangential retardation of the particle and the normal acceleration of the particle are equal. If its speed at t = 0 i s v 0 , the time taken to complete the first revolution is
Options
- AR v 0
- BR v 0 ( 1 - e - 2 π )
- CR v 0 e - 2 π
- D2 π R v 0
Correct answer
B. R v 0 ( 1 - e - 2 π )
Step-by-step solution
When a particle moves in a circular motion, it is acted upon by centripetal force directed towards the centre. Hence, centripetal acceleration is a N = d v d t = v 2 R o r     ∫ 0 t d t R = ∫ v 0 v d v v 2 o r       t = - R 1 v v 0 v v = v 0 R R - v 0 t A l s o         d r d t = v 0 R R - v 0 t ∫ 0 2 π   R d r = v 0 R   ∫ 0 T d t R - v 0 t ⟹       T = R v 0 1 - e - 2 π