A sphere is rolling without slipping on a fixed horizontal plane surface. In Fig. `A` is the point of contact `B` is the centre of the sphere and `C` is its topmost point. Then,

Options

A. `vecV_(C) - vecV_(A) =2(vecV_(B)-vecV_(c))`
B. `vecV_(c)-vecV_(B) = vecV_(B) -vecV_(A)`
C. `|vecV_(C) - vecV_(A)| =2|(vecV_(B) - vecV_(C))|`
D. `|vecV_(c)-vecV_(A)| =4|vecV_(B)|`

Answer

B, C

Explanation

`V_(A) =0, V_(B) =omegar, V_(C) = 2omegar`
`vecV_(C) - vecV_(A)` is towards the right and `vecV_(B)- vecV_(C)` is towards left,
Hence, option (A) is incorrect, But in magnitude, option (C ) is correct.
`vecV_(C) -vecV_(A) = 2omega r = 2vecV_(B)`