Question #42237

A solid sphere of external radius $R$ and a concentric internal cavity of radius $R_c$ is completely submerged in a liquid of constant density $\rho_L$. The sphere is held in equilibrium by a thin vertical wire. The interatomic potential of the solid's material near its equilibrium atomic spacing $r_0$ is modeled as $U(r) = U_0 + \frac{1}{2}k(r-r_0)^2 - b(r-r_0)^3$, where $k$ and $b$ are positive constants and $r$ is the interatomic distance. If the temperature of the system is increased by a small amount $\Delta T$, which of the following represents the change in the buoyant force $\Delta F_B$ acting on the sphere? (Assume the liquid's density is unaffected by temperature, $k_B$ is the Boltzmann constant, and $g$ is the acceleration due to gravity.)