A disc rolls on ground without slipping. Velocity of centre of mass is `v`. There is a point P on circumference of disc at angle `theta`. Suppose, `v_(P)` is the speed of this point. Then, match the following columns

`{:(,"Column-I",,"Column-II"),("(A)","If" theta=60^(@),"(p)",v_(P)=sqrt(2)v),("(B)","If" theta=90^(@),"(q)",v_(P)=v),("(C)","If" theta=120^(@),"(r)",v_(P)=2v),("D)","If" theta=180^(@),"(s)",v_(P)=sqrt(3)v):}`

Answer

`(A rarrq,B rarr p,C rarrs,D rarr r)`

Explanation

In gerenal as `v_(P)=2v sin((theta)/(2))`
If `theta=90^(@)`, then `v_(P)=2v sin ((60^(@))/(2))=2vxx(1)/(2)=v`
`rArr (A) rarr (q)`
If `theta = 90^(@)`, then `v_(P) =2v sin ((90^(@))/(2))=2v xx (1)/(sqrt(2))=sqrt(2)v`
`rArr (B) rarr (p)`
If `theta =120^(@)`, then `v_(P) = 2 v sin ((120^(@))/(2))=2vxx(sqrt(3))/(2)=sqrt(3)v`
`rArr (C) rarr (s)`
If `theta =180^(@)`, then `v_(P) =2v sin ((180^(@))/(2))=2v rArr (D)rarr (r)`.