**Understanding the Fate of Our Sun**After the Sun exhausts its nuclear fuel, it may collapse into a white dwarf. This state maintains approximately the same mass as the Sun now but with a radius close to that of Earth's.(a) **Calculating Average Density:**To find the average density of the white dwarf when the Sun collapses to a radius of \(6.31 \times 10^6\) m:- Initial answer: \(1.84 \times 10^9\) kg/m\(^3\) (incorrect).- Note: The response is within 10% of the correct value, possibly due to roundoff error. Use at least four-digit accuracy in calculations to minimize such errors.(b) **Free-Fall Acceleration:**Calculate the free-fall acceleration at its surface.- Correct answer: \(3.27 \times 10^6\) m/s\(^2\).(c) **Gravitational Potential Energy:**Determine the gravitational potential energy of a \(4.00\) kg object at its surface, assuming \(U_g = 0\) at infinity.- Correct answer: \(-8.33 \times 10^{13}\) J.**Help and Resources:**For further assistance, refer to additional educational resources or seek expert guidance.

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After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state, in which it has approximately the same mass as it has now but a radius equal to roughly the size of the Earth's radius. (a) Calculate the average density of this white dwarf if the Sun were to collapse to a radius of 6.31 × 10°m. 1.84e+9 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. kg/m (b) Calculate the free-fall acceleration at its surface. 3.27e+6 m/s2 (c) Calculate the gravitational potential energy of a 4.00 kg object at its surface. (Take U, = 0 at infinity.) -8.33e+13 Need Help? Read It

After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state, in which it has approximately the same mass as it has now but a radius equal to roughly the size of the Earth's radius. (a) Calculate the average density of this white dwarf if the Sun were to collapse to a radius of 6.31 × 10°m. 1.84e+9 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. kg/m (b) Calculate the free-fall acceleration at its surface. 3.27e+6 m/s2 (c) Calculate the gravitational potential energy of a 4.00 kg object at its surface. (Take U, = 0 at infinity.) -8.33e+13 Need Help? Read It