   Chapter 7, Problem 36P

Chapter
Section
Textbook Problem

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 Earth. Calculate (a) the average density of the while dwarf, (b) the surface free-fall acceleration, and (c) the gravitational potential energy associated with a 1.00-kg object at the surface of the white dwarf.

(a)

To determine
The average density of the white dwarf.

Explanation

Given info: The mass of the dwarf is 1.991×1030kg and the radius of the dwarf is 6.38×106m .

Explanation: The average density of the dwarf is defined as ρ=MSun/VEarth=MSun/[(4/3)πREarth3] but in this case the mass of the sun remains constant after the collapse to a white dwarf state and its volume is reduced to the volume of the earth.

The formula for the average density of the white dwarf is,

ρ=3Mdwarf4πRdwarf3

• Mdwarf is mass of the dwarf.
• Rdwarf is radius of the dwarf.

Substitute 1.991×1030kg for Mdwarf and 6

(b)

To determine
The surface free acceleration of the white dwarf.

(c)

To determine
The gravitational potential energy associated with 1.00kg object on the surface of the white dwarf.

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