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) isthe 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):}

A disc rolls on ground without slipping. Velocity of centre of mass is

1.	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) isthe 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» SOLUTION :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)`.