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 \frac{v_B}{v_A}=\sqrt{\frac{10 n}{15^{1 \/ 3}}}. The value of n is [JEE Adv 2022 P1]

Gravitation

Section: Physics

Question : 5 of 21

Marks: +1, -0

Two spherical stars A and B have densities ρA and ρB, respectively. A and B have the same radius, and their masses MA and MB are related by MB=2MA. 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. The entire mass lost by A is deposited as a thick spherical shell on B with the density of the shell being ρA. If vA and vB are the escape velocities from A and B after the interaction process, the ratio ‌

=√‌

10n

151∕3

. The value of n is

[JEE Adv 2022 P1]

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