Question

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

A. `vacV_C - vacV_A = 2 (vacV_B - vac_C)`
B. `vacV_C - vacV_B = vac_B - vac_A`
C. `|vacV_C - vac_A| = 2|vacV_B - vac_C|`
D. `|vacV_C - vacV_A| = 4 |vacV_B|`

Answer 1

Correct Answer - B::C
(b,c)
`If vecV_0` is the velocity of centre of the sphere, then
`vecV_C = 2vecV_0 , vec_B = vecV_0 and vec_A = 0`
`:. vecV_C - vecV_B = 2vecV_0 - vecV_0 = vecV_0`
`vecV_B - vecV_A = vecV_0 - vec0 = vecV_0`
`:. vecV_C - vecV_B = vecV_B - vecV_A`
(b) is the correct opton.
Now, `|vecV_C - vecV_A |=|2vecV_0 - 0 |=|2vecV_0 |=2|vecV_0|`
and `|vecV_C - vecV_A| =2|vecV_B - vecV_C|`
(c ) is the correct option.