A ring rolls without slipping on the ground. Its centre `C` moves with a constant speed `u.P` is any point on the ring. The speed of `P` with respect to the ground is `v`.

Options

A. `0levle2u`
B. `v=u,` if `CP` is horizontal
C. `v=u`, if `CP` makes an angle of `30^@` with the horizontal and `P` is below the horizontal level of `C`.
D. `v=sqrt(2)u,` if `CP` is horizontal

Answer

A, C, D

Explanation

Net velocity of `P`
`v=sqrt(u^(2)+u^(2)+2u.ucos(180-theta))`
`=usqrt(2-2costheta)`
For `theta=0^@,v=0`
For `theta=180^@,v=2u`
For `theta=90^@,v=sqrt(2)u`
For `v=u`
`usqrt(2-2costheta)=uimpliescostheta=1/2impliestheta=60^@`