Answer:
dA/dB = 4.955
Approximately, the ratio is 5/1
(Where dA is mean density for planet A while dB is mean density for planet B)
Explanation:
Mass of A = mA
Mass of B = mB
mA/mB = 0.96
Mean radius for A = mA = (8.1 × 10^3)/2 = 4.05 × 10^3 km
Mean radius for B = mB = (1.4 × 10^4)/2
= 7×10^3km
Density = mass/volume
Volume of a sphere = 4/3Πr3
Mean volume for A = (4/3) × Π × (4.05 × 10^3)^3
= 2.784 × 10^11 km3
Mean volume for B = 4/3×Π×(7×10^3)^3
= 1.437 × 10^12km3
Since m/v = d ( where m = mass, v = volume and d = density)
mA = 2.784 × 10^11 km3 × dA ...equation 1
mB= 1.437 × 10^12km3 × dB... equation 2
but mA/mB= 0.96
mA = 0.96 × mB
substitute for mA in equation 1
0.96 × mB = 2.784 × 10^11 x dA equation 3
Substitute for mB in equation 3..
(refer to equation 2)
0.96×1.437×10^12 × dB = 2.784 × 10^11 × dA .....equation 4
divide through by the coefficient of dA
dA = (0.96×1.437×10^12×dB)/(2.784 × 10^11)
divide through by dB
dA/dB = 4.955
therefore, the ratio of dA to dB is 5/1
Therefore, the mean density of A is almost five times that of B