1) 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 (1ρdρdt) is constant. The velocity v of any point of the surface of the expanding sphere is proportional to A) R B) 1R C) R2 D) R23 Answer: Option AExplanation:m=4πR33×ρ On taking log both sides, we have ln(m)= ln((4π3)) + ln(ρ)+3ln(R) On differentiating with respect to time 0=0+1ρdρdt+3RdRdt ⇒ (dRdt)=v∝−R×1ρ(dρdt) v∝R