The condition for the uniform sphere of mass m of radius r to be a black hole is (G = gravitational constant) :

Options

A. `((2Gm)/(r ))^(1//2) ge C`
B. `((2Gm)/(r ))^(1//2) le C`
C. `((2gm)/(r ))^(1//2) = C`
D. `((gm)/(r ))^(1//2) ge C`

Answer

A

Explanation

We know that condition for a star or sphere to be black hole is `(Gm)/(rc^(2)) ge (1)/(2)`, where c is speed of light.
`therefore ((2Gm)/(r ))^(1//2) ge c`.
Thus correct choice is (a).