Topic: Rigid Bodies
Concepts: Floating, Gauss’s law for gravity, Gravitational force, Rolling down inclined plane

Solution:

• A) Not correct since by the shell theorem, the gravitational field outside a solid sphere or spherical shell is identical to that of a point located at the center with the same mass. Thus, orbits around both objects are identical.
• B) Correct since the acceleration of an object rolling down an inclined plane is given by
  
  $a=\frac{g\sin\theta}{1+\beta}$
  
  
  
  where the object has moment of inertia $I=\beta mr^2$. For a solid sphere, $\beta=2/5$ while for a spherical shell, $\beta=2/3$. Since the solid sphere has a smaller $\beta$, it has a larger acceleration and takes less time to roll down the inclined plane.
• C) Not correct since by the shell theorem, the gravitational field outside a solid sphere or spherical shell is identical to that of a point located at the center with the same mass. Thus, tidal forces exerted by both objects are identical.
• D) Not correct since the fraction of an object that floats is
  $f_{\text{float}}=1-f_{\text{sub}}=1-\frac{\rho_{\text{obj}}}{\rho_{\text{wat}}}$. Both objects have the same shape and mass so they have the same average density and therefore $f_{\text{float}}$.
  
  
  
• E) Not correct since in a uniform gravitational field $g$, the force applied to an object of mass $m$ is
  
  $F=mg$
  
  Since both objects have the same mass, they experience the same force.

Thus, the answer is B.