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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:

→VC−→VA=2(→VB−→VC)

|→VC−→VA|=2|→VB−→VC|

→VC−→VB=→VB−→VA

|→VC−→VA|=4|→VB|A

Solution:

→VA−→VB=→rA×→ωand →VC−→VB=→rC×→ωand →rA=−→rc
→VA−→VB=−(→VC−→VB)
||→VA−→VB||=||→VC−→VB||and →VC−→VA=(→rC−→rA)×→ω=2→rC×→ω=2(→VC−→VB)