Two spherical stars A and B have densities \( \rho_A \) and \( \rho_B \), respectively. A and B have the same radius, and their masses \( M_A \) and \( M_B \) are related by \( M_B = 2 M_A \). Due to an interaction process, star A loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains \( \rho_A \). The entire mass lost by A is deposited as a thick spherical shell on B with the density of the shell being \( \rho_A \). If \( v_A \) and \( v_B \) are the escape velocities from A and B after the interaction process, the ratio \( \dfrac{v_B}{v_A} = \sqrt{\dfrac{10 n}{15^{1/3}}} \). The value of \( n \) is:
