since sphere is not slipping on the plank hence acc. of plank = acc. of the bottomost point.

 

now let the acc. of centre of sphere be acm

 

hence acm + Ralpha = acc. of bottomost point = acc. of plank

 

hence acm = acc.of plank - Ralpha

 

hence a) is correct

 

b) is correct as friction is the only force causing movement of the sphere

 

c) is correct as only external force is F

 

hence ans is D)