Question

A block hole is a body from whose surface nothing may even escape. What is the condition for a uniform spherical body of mass `M` to be a block hole? What should be the radius of such a black hole if its mass is nine times the mass of the earth?
Mass of earth `= 6xx 10^(24)kg`,
`G = 6.61 xx 10^(-11) Nm^(2) kg^(-2)`.

Answer 1

According th theory of relativity, no object can move with a speed greater than the speed of light `c (= 3 xx 10^(8) m//s)`. It means `c` is the upper limit to the projectile escape velocity.
hence for a body to act as a black hole
`upsilon_(e) = sqrt((2 GM)/(R )) le c` or `R = (2 GM)/(c^(2))`
If `M = 9 M_(E) = 9 xx 6 xx 10^(24) kg`, then
`R = (2 xx (6.67 xx 10^(-11)) xx (9 xx 6 xx 10^(24)))/((3 xx 10^(8))^(2))`
`= 8 xx 10^(-2) m 8 = cm `