After the Sun exhausts its nuclear fuel, its ultimate fate will be to collapse t
ID: 2199015 • Letter: A
Question
After the Sun exhausts its nuclear fuel, its ultimate fate will be to collapse to a white dwarf state. In this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of the Earth. (a) Calculate the average density of the white dwarf. . Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. kg/m3 (b) Calculate the surface free-fall acceleration. . m/s2 (c) Calculate the gravitational potential energy associated with a 1.24-kg object at the surface of the white dwarf.Explanation / Answer
After making a simplifying assumption that the mass of the Sun is maintained and only a very insignificant of its mass is lost to the universe, (a) average density, d, of sun when turned into a white dwarf = (1.99*10^30)/[(4*pi/3)(6.03*10^6)^3] or d = 2.17*10^9 kg/m^3 (b) free fall acceleration = [(6.67*10^-11)*(1.99*10^30)]/(6.03*10^6)… = 3.65*10^6 m/s (c) required energy = - [(6.67*10^-11)*(2.00)*(1.99*10^30)]/(6.0… = - 4.40*10^12 J