A particle is moving in a circle of radius R in such a way that at any instant the normal and the tangential component of its acceleration are equal. If its speed at t = 0 is v 0 then the time it ta

Question

A particle is moving in a circle of radius R in such a way that at any instant the normal and the tangential component of its acceleration are equal. If its speed at t = 0 is v 0 ​ then the time it takes to complete the first revolution is α v 0 ​ R ​ ( 1 − e − β π ) . Find the value of ( α + β ) 6 .

TestHub · Accepted Answer

dt dv ​ ∫ v 0 ​ v ​ v 2 dv ​ v dt ds ​ ∫ 0 2 π R ​ ds 2 π R 1 − R v 0 ​ ​ t t α ( α + β ) 6 ​ = R v 2 ​ = R 1 ​ ∫ 0 t ​ dt = 1 − R v 0 ​ ​ t v 0 ​ ​ = 1 − R v 0 ​ ​ t v 0 ​ ​ = ∫ 0 t ​ ( 1 − R v 0 ​ ​ t ) v 0 ​ ​ dt = − R [ ln ( 1 − R v 0 ​ ​ t ) ] 0 t ​ = e − 2 π = v 0 ​ R ​ ( 1 − e − 2 π ) = 1 , β = 2 = ( 1 + 2 ) 6 = 729 ​

Physics - Circular Motion Question with Solution | TestHub

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