Two points at the same time began to move with the same constant velocity `V=pi m//s`, a circle fo radius r=1 m, the other on a circle of radius R=2m (figure). Find the time (in sec) after which they will be again on same position together.

Answer

5

Explanation

`v=romega_(1)`
`v=2 r omega_(2)`
`omega_(1)=v/r`
`omega_(2)=v/(2r)`
`theta_(1)=(vt)/r`
`theta_(2)=(vt)/(2r)`
`theta_(1)=2pi+(vt)/(2r)`
`(vt)/r=2p+(vt)/(2r)`
`(vt)/(2r)=2pi`
`t=(4pir)/v=(4xxpixx1)/(pi)=4 sec`.