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

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**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.
Transcribed Image Text:**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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