Answer:
(a) 2 × 10^9 kg/m^3; (b) roughly the mass of the Statue of Liberty.
Step-by-step explanation:
(a) Density of white dwarf:
D = m/V
Data:
1 solar mass = 2 × 10^30 kg
1 Earth radius = 6.371 × 10^6 m
Calculations:
V = (4/3)πr^3 = (4/3)π × (6.371 × 10^6 m)^3 = 1.083 × 10^21 m^3
D = 2 × 10^30 kg/1.083 × 10^21 m^3 = 2 × 10^9 kg/m^3
2. Weight on a white dwarf
The formula for weight is
w = kMm/r^2
where
k = a proportionality constant
M = mass of planet
m = your mass
w(on dwarf)/w(on Earth) = [kM(dwarf)m/r^2] /[kM(Earth)m/r^2
k, m, and r are the same on both planets, so
w(on dwarf)/w(on Earth) = M(dwarf)/M(Earth)
w(on dwarf) = w(on Earth) × [M(dwarf)/M(Earth)]
Data:
M(Earth) = 6.0 × 10^24 kg
Calculation:
w(on dwarf) = w(on Earth) × (2 × 10^30 kg /6.0 × 10^24 kg)
= 3.3 × 10^5 × w(on Earth)
Thus, if your weight on Earth is 60 kg, your weight on the white dwarf will be
3.3 × 10^5 × 60 kg = 2 × 10^7 kg
That's roughly as heavy as the Statue of Liberty is on Earth.
