Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density ρ remains uniform throughout the volume. The rate of fractional change in density 1 ρ d ρ d t is constant. The velocity v of any point on the surface of the expanding sphere is proportional to

Question

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density ρ remains uniform throughout the volume. The rate of fractional change in density 1 ρ d ρ d t is constant. The velocity v of any point on the surface of the expanding sphere is proportional to, R 3, 1 R, R, R 2 3

MARKS App · Accepted Answer

Density of sphere is ρ = m v = 3 m 4 π R 3 ⇒ 1 ρ d ρ d t = - 3 R d R d t Since ⇒ 1 ρ d ρ d t is constant ∴ d R d t ∝ R

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