Question

A sphere of radius R is rolling on a rough horizontal surface. The magnitude of velocity of A with respect to ground will be

A. `sqrt(2)v_(CM)`
B. 2`V_(CM)sintheta`
C. `sqrt(2)v_(CM)sqrt(1+sintheta)`
D. No sufficient information

Answer 1

c) Here `v_(CM) = Romega`
`The resultant velocity of point A is
`v_(A) = sqrt(v_(CM)^(2) + (Romega)^(2) + 2v_(CM)(Romega)cos(90-theta))`
`=sqrt(v_(CM)^(2) + v_(CM)^(2) + 2v_(CM)^(2)sintheta)`
`sqrt(2)v_(CM)sqrt(1+sintheta))`