A particle is moving in a circle of raidus R in such a way that at any instant the total acceleration makes an angle of $$450$$ with radius. Initial speed of particle is $$v0$$. The time taken to complete the first revolution is:

Question

A particle is moving in a circle of raidus R in such a way that at any instant the total acceleration makes an angle of $$450$$ with radius. Initial speed of particle is $$v0$$. The time taken to complete the first revolution is:

Infinity Learn · Accepted Answer

Total acceleration makes an angle of $$450$$ with radius,i.e., tangential acceleration $$=$$ radial acceleration.Rα $$=$$ Rω$$2or$$ α $$=$$ ω$$2or$$ dωdt $$=$$ ω$$2or$$ dωω$$2$$ $$=$$ dtor ∫ω$$0$$ωdωω$$2$$ $$=$$ ∫$$0tdt$$ω $$=$$ ω$$01-$$ω$$0tor$$ dθdt  $$=$$ ω$$01-$$ω$$0tor$$ ∫$$02$$$$π$$dθ $$=$$ ∫$$0t$$ω$$0dt1-$$ω$$0tor$$ t $$=$$ $$1$$ω$$0(1-e-2$$π$$)$$ $$=$$ $$Rv0(1-e-2$$π$$)$$

A particle is moving in a circle of raidus R in such a way that at any instant the total acceleration makes an angle of $45^{0}$ with radius. Initial speed of particle is $v_{0}$ . The time taken to complete the first revolution is:

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A particle is moving in a circle of raidus R in such a way that at any instant the total acceleration makes an angle of 450 with radius. Initial speed of particle is v0. The time taken to complete the first revolution is:

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A particle is moving in a circle of raidus R in such a way that at any instant the total acceleration makes an angle of $45^{0}$ with radius. Initial speed of particle is $v_{0}$ . The time taken to complete the first revolution is: