Which of the following can be used to distinguish a solid ball from a hollow sphere of the same radius and mass?

$\textbf{(A)}$ Measurements of the orbit of a test mass around the object.
$\textbf{(B)}$ Measurements of the time it takes the object to roll down an inclined plane. 
$\textbf{(C)}$ Measurements of the tidal forces applied by the object to a liquid body.
$\textbf{(D)}$ Measurements of the behavior of the object as it oats in water.
$\textbf{(E)}$ Measurements of the force applied to the object by a uniform gravitational field.
To determine which option can be used to distinguish a solid ball from a hollow sphere of the same radius and mass, we need to analyze each option carefully.

1. **Option A: Measurements of the orbit of a test mass around the object.**
   - The gravitational force exerted by an object depends only on its mass and the distance from the object. Since both the solid ball and the hollow sphere have the same mass and radius, the gravitational force they exert on a test mass would be identical. Therefore, the orbit of a test mass around either object would be the same.
   - Hence, this option cannot distinguish between the two objects.

2. **Option B: Measurements of the time it takes the object to roll down an inclined plane.**
   - The time it takes for an object to roll down an inclined plane depends on its moment of inertia. The moment of inertia for a solid ball and a hollow sphere are different.
     - For a solid ball of mass \(M\) and radius \(R\), the moment of inertia \(I_{\text{solid}}\) is given by:
       \[
       I_{\text{solid}} = \frac{2}{5}MR^2
       \]
     - For a hollow sphere of mass \(M\) and radius \(R\), the moment of inertia \(I_{\text{hollow}}\) is given by:
       \[
       I_{\text{hollow}} = \frac{2}{3}MR^2
       \]
   - Since the moments of inertia are different, the acceleration and thus the time it takes to roll down an inclined plane will be different for the two objects.
   - Therefore, this option can distinguish between the two objects.

3. **Option C: Measurements of the tidal forces applied by the object to a liquid body.**
   - Tidal forces depend on the mass distribution of the object and the distance from the object. However, for objects of the same mass and radius, the tidal forces at a given distance would be very similar and difficult to distinguish with simple measurements.
   - This option is too complex and not practical for distinguishing between the two objects with basic physics knowledge.

4. **Option D: Measurements of the behavior of the object as it floats in water.**
   - The behavior of an object floating in water depends on its density and buoyancy. Since both objects have the same mass and volume, their densities are the same, and they would float in the same manner.
   - Therefore, this option cannot distinguish between the two objects.

5. **Option E: Measurements of the force applied to the object by a uniform gravitational field.**
   - The force applied to an object by a uniform gravitational field depends only on its mass. Since both objects have the same mass, the force applied to them would be identical.
   - Therefore, this option cannot distinguish between the two objects.

Based on the analysis, the only option that can distinguish between a solid ball and a hollow sphere of the same radius and mass is option B, due to the difference in their moments of inertia.

The final answer is $\boxed{\textbf{(B)}}$.