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Imagine that the entire Sun, of mass MS , collapses to a sphere of radius Rg such that the work required to remove a small mass m from the surface would be equal to its rest energy mc² . This radius is called the gravitational radius for the Sun.(a) Use this approach to show that Rg = GMS / c² .

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It is proved for gravitational radius that Rg=GMs/c^2 .

Given,

The mass of sun = Ms

Sphere of radius = Rg

Sun collapses to a sphere such that the work required to remove a small mass (m) from the surface would be equal to its rest energy mc^2 .

The given radius (Rg) is called as gravitational radius for sun.

We know,

gravitational potential energy Ug = G ×Ms×m/Rg

given, the rest energy, E =mc^2

As it is given that work required to remove small mass is equal to rest energy,

thus, Ug=E

G×Ms×m/Rg = mc^2

Rg =GMs/c^2

Hence, it is proved for gravitational radius that Rg=GMs/c^2 .

What is gravitational potential energy?

Total work done in assembling bodies together,in their respective places, is called gravitational potential energy of the system.

Learn more about gravitational potential energy here:

brainly.com/question/21555779

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