A) \[\frac{2G{{M}_{e}}}{{{C}^{2}}}\]
B) \[\frac{2G{{M}_{e}}}{3{{C}^{2}}}\]
C) \[\frac{G{{M}_{e}}}{3{{C}^{2}}}\]
D) \[\frac{G{{M}_{e}}}{{{C}^{2}}}\]
Correct Answer: A
Solution :
The Schwarzschild radius is proportional to the mass (Mg) with a proportionality constant involving the gravitational constant (G) and the speed of light \[{{r}_{s}}=\frac{2G{{M}_{e}}}{{{C}^{2}}}\]where,\[{{r}_{s}}\] is the Schwarzschild radius, G is the gravitational constant, \[{{M}_{e}}\] is the mass of the object, C is the speed of light in vacuum. The proportionality constant, \[2G/{{C}^{2}}\] is Approximately \[1.48\times {{10}^{-27}}m/kg\], or 2.95 km/solar mass. An object of any density can be large enough to fall within its own Schwarzschild radius.
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