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 ((1/rho) (drho/dt)) is constant. The velocity v of any point on the surface of the expanding sphere is
proportional to
[A] R [B] R³ [C] 1/R [D] R²/³
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Answer:
Hope it help
ρ=
Volume
Mass
Mass=ρ×Volume=constant
On differentiating,
V
dt
dρ
+ρ
dt
dV
=0
3
4
πR
3
×
dt
dρ
+ρ×
dt
d
(
3
4
πR
3
)=0
ρ
1
dt
dρ
=
R
−3
dt
dR
dt
dR
∝R
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