A small sphere is suspended by a string from the ceiling of a car. If the car begins to move with constant acceleration a, the inclination of the string to the vertical is:
(A) tan^(-1)(a/g) in the direction of motion.
(B) tan^(-1)(a/g) opposite to the direction of motion.
(C) tan^(-1)(g/a) in the direction of motion.
(D) tan^(-1)(g/a) opposite to the direction of motion.

When the car accelerates with a constant acceleration \( a \), the small sphere suspended by a string will not hang vertically but will make an angle with the vertical. To find this angle, consider the following analysis:

1. **Forces Acting on the Sphere**:
- **Gravity (mg)**: Acts downward.
- **Tension (T)**: Acts along the string.
- **Pseudo-force**: Due to the car's acceleration, there is a pseudo-force acting on the sphere in the direction opposite to the car's acceleration, which is \( ma \).

2. **Equilibrium in the Accelerating Frame**:
- The pseudo-force and the gravitational force create a resultant force that has to be balanced by the tension in the string.
- The tension \( T \) in the string has two components:
- \( T \cos \theta \): Balances the gravitational force.
- \( T \sin \theta \): Balances the pseudo-force due to acceleration.

Therefore:
\[
T \cos \theta = mg
\]
\[
T \sin \theta = ma
\]

3. **Finding the Angle**:
- Divide the second equation by the first:
\[
\frac{T \sin \theta}{T \cos \theta} = \frac{ma}{mg}
\]
\[
\tan \theta = \frac{a}{g}
\]

Hence, the angle \( \theta \) that the string makes with the vertical is:
\[
\theta = \tan^{-1} \left( \frac{a}{g} \right)
\]

4. **Direction of the Inclination**:
- The string inclines in the direction of the car's acceleration.

Thus, the correct answer is:

**(A) \(\tan^{-1}\left( \frac{a}{g} \right)\) in the direction of motion.**