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 A

Explanation:

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)=vR×1ρ(dρdt)

    vR