JEE (Advanced) 2017 Paper-2 Question 1

Question 1

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $$\rho$$ remains uniform throughout the volume. The rate of fractional change in density $$(\frac{1}{\rho}\frac{d\rho}{dt})$$ is constant. The velocity $$\nu$$ of any point on the surface of the expanding sphere is proportional to

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