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Two spherical stars A and B have densities rho_A and rho_B. They start with the same radius, and their masses satisfy M_B = 2*M_A. In an interaction, star A loses mass so that its radius becomes half its original value while staying spherical and keeping its density rho_A. All the mass shed by A is added onto B as a thick uniform spherical shell of density rho_A. Let v_A and v_B be the escape speeds from A and B after this process. If v_B/v_A = sqrt(10n / 15^(1/3)), find the value of n.
- 2.3
- 1.5
- 4.6
- 3.0
Correct answer: 2.3
Solution
Track masses and radii after the redistribution, then use the escape-velocity formula. The new radius of B comes from adding the shed volume (mass/density rho_A) to B's original volume.
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