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 .
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