Q. Two spherical stars and have densities and , respectively. and have the same radius, and their masses and are related by . Due to an interaction process, star loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains . The entire mass lost by is deposited as a thick spherical shell on with the density of the shell being . If and are the escape velocities from and after the interaction process, the ratio . The value of is ___

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Answer: 2.30

Solution:

Given

Calculation of escape velocity for :
Radius of remaining star .
Mass of remaining star


Calculation of escape velocity for
Mass collected over
Let the radius of B becomes .