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JEE Advanced 2022 Physics question

PhysicsGravitationJEE Advanced 2022

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 .

Answer: 2.3

Solution

Let the common radius be . With density unchanged and radius halved, A's mass becomes ; the mass lost, , has volume (density ). Deposited on B as a shell: $Missing argument for \frac\frac43π(R'^3- = Missing argument for \frac\frac78·Missing argument for \frac\frac43π ⇒ R'^3 = ⇒

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Question ID VK-033972