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Question Number 16497 by Tinkutara last updated on 23/Jun/17

$$\mathrm{Two}\mathrm{particles}\mathrm{are}\mathrm{revolving}\mathrm{on}\mathrm{two}$$$$\mathrm{coplanar}\mathrm{circles}\mathrm{with}\mathrm{constant}\mathrm{angular}$$$$\mathrm{velocities}{\omega }_1\mathrm{and}{\omega }_2\mathrm{respectively}.\mathrm{Their}$$$$\mathrm{time}\mathrm{periods}\mathrm{are}{T}_1\mathrm{and}{T}_2\mathrm{then}\mathrm{prove}$$$$\mathrm{that}\mathrm{the}\mathrm{time}\mathrm{taken}\mathrm{by}\mathrm{second}\mathrm{particle}$$$$\mathrm{to}\mathrm{complete}\mathrm{one}\mathrm{revolution}\mathrm{more}\mathrm{than}$$$$\mathrm{the}\mathrm{first}\mathrm{particle},T,\mathrm{is}\mathrm{given}\mathrm{by}$$$$T=\frac{T_1{T}_2}{T_1-T_2}$$

Answered by ajfour last updated on 23/Jun/17

$$△t=\frac{2\pi }{△\omega }=\frac{2\pi }{(\frac{2\pi }{T_2}-\frac{2\pi }{T_1})}=\frac{T_1{T}_2}{T_1-T_2}.$$

Commented by Tinkutara last updated on 23/Jun/17

$$\mathrm{Thanks}\mathrm{Sir}!$$

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