Answer
The force on the sphere from the wall is $~~4.4~N$
Work Step by Step
In part (a) we found that the tension in the rope is $9.4~N$
We can find the angle $\theta$ that the rope makes with the vertical:
$tan~\theta = \frac{4.2~cm}{8.0~cm}$
$\theta = tan^{-1}~(\frac{4.2~cm}{8.0~cm})$
$\theta = 27.7^{\circ}$
The horizontal component in the rope's tension $F_T$ is equal in magnitude to $F_w$, the force on the sphere from the wall. We can find $F_w$:
$F_w = F_T~sin~\theta$
$F_w = (9.4~N)~sin~27.7^{\circ}$
$F_w = 4.4~N$
The force on the sphere from the wall is $~~4.4~N$
