Let a' be the acceleration of the sphere's cm wrt the wedge. It will be directed down the plane. Let a be the acceleration of the wedge. Let
be the angular acceleration of the sphere. Now as the sphere is observed in the reference frame of the wedge, there is a pseudo force ma on the sphere directed opposite to the acceleration of the wedge.
If N be the normal force between the sphere and the wedge,
N=mg cos
- ma sin
and Nsin
= ma
This gives a = gsin
cos
/(1+sin2
)
Now, for no slipping a' =
R
a cos
+ g sin
- (f/m) = (5f/2m)
Substitute the value of a and find f