Answer
(a) $a=g\tan\theta$
(b) $a=1.73m/s^2$
(c) $\theta=0^o$
Work Step by Step
(a) As the van accelerates with acceleration $a$ forward, the sphere swings backward with similar acceleration $a$. On horizontal side, if we call the force that pushes the sphere backward $F$, we have $$F=m_{sphere}a$$
Similarly, on vertical side, the sphere is under its weight: $$W=m_{sphere}g$$
Angle $\theta$ can be found by taking the tangent of the horizontal over the vertical: $$\tan\theta=\frac{F}{W}=\frac{a}{g}$$ $$a=g\tan\theta$$
(b) When $\theta=10^o$, $a=g\tan10=1.73m/s^2$
(c) If the van moves with constant velocity, its acceleration $a=0$, which means $$g\tan\theta=0$$ $$\tan\theta=0$$ $$\theta=0^o$$
