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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.
(b) Find a numerical value for Rg .

Sagot :

tanisharawat014

The value of radius (Rg) is 1.475km .

Given,

The mass of the sun = Ms

Radius of the sphere = Rg

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 the gravitational radius for the sun.

We know,

Gravitational potential energy or work done

= Ug = GMs×m/Rg

the given rest energy = E =mc^2

As, it is given that the required work or energy is equal to rest energy,

thus, Ug=E

GMs×m/Rg = mc^2

Rg = GMs/c^2

We know,

G = 6.67×10^-11 N. m^2/kg^2

Ms = 1.99×10^30 kg

c = 3×10^8 m/s

Thus, Rg = 6.67×10^-11 × 1.99×10^30 / (3×10^8)^2

Rg = (13.2733×10^19)/(9×10^16 )

Rg = 1.4748×10^3 m

Rg = 1.475km

Hence, The value of radius (Rg) is 1.475km .

Learn more about gravitational potential energy here:

brainly.com/question/21555779

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