Two spherical stars A and B have densities and

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

Two spherical stars A and B have densities ρA\rho_A and ρB\rho_B, respectively. A and B have the same radius, and their masses MAM_A and MBM_B are related by MB=2MAM_B = 2M_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 ρA\rho_A. The entire mass lost by A is deposited as a thick spherical shell on B with the density of the shell being ρA\rho_A. If vAv_A and vBv_B are the escape velocities from A and B after the interaction process, the ratio vBvA=10n151/3\frac{v_B}{v_A} = \sqrt{\frac{10n}{15^{1/3}}}. The value of nn is ____.

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