After the Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to

Question

After the Sun exhausts its nuclear fuel, its ultimate fate may 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. 1.838e9 Correct: Your answer is correct. kg/m3

(b) Calculate the surface free-fall acceleration. 3.26e6 Correct: Your answer is correct. m/s2

(c) Calculate the gravitational potential energy associated with a 4.61-kg object at the surface of the white dwarf. -3.87e16 Incorrect: Your answer is incorrect. I figured out A and B on my own but I could not figure out part C for this question

Explanation / Answer

The mass of the sun is: 1.99* 10^30 kg
The radius of the Earth is: 6371 km

Potential energy of sun
U = -(G*M*m/r)
U = -(6.67*10^-11 N m^2/kg^2)*(1.99*10^30kg)*(4.61kg) /(6371km)
U = -9.6*10^16 J

But according to you as you find density = 1.838*10^9

so, mass become = (4*pi*r^3/3)*1.838*10^9

= 5.97*10^21 kg

so potential energy would be

U = -(G*M*m/r)
U = -(6.67*10^-11 N m^2/kg^2)*( 5.97*10^21 kg )*(4.61kg) /(6371km)
U = -2.88*10^8 J

Check which one is correct

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